SAS proc mixed 过程步介绍
SAS过程步及常用语句
SAS过程步简介SAS过程步的一般形式为：PROC 过程名 [ DATA=输入数据集] [选项];过程语句1 [/ 选项 ];过程语句2 [/ 选项];……RUN;1．VAR语句VAR语句在过程步中用于指定分析变量。
VAR语句的语法格式为：VAR 变量名1 变量名2 … 变量名n;变量名列表可以使用省略的形式，如x1-x3 等。
应用实例：var math chinese;2．MODEL语句MODEL语句在统计建模过程中用来指定模型的形式。
语法格式为：MODEL 因变量 = 自变量列表 / 选项; 应用实例：model y=x1 x2 x3 ;3．BY语句BY语句在过程步中用来指定一个或几个分组变量，根据这些分组变量值可以把观测记录分组，然后对每一组观测分别进行指定的分析。
在使用带有BY语句的过程步之前，应先用SORT过程按BY语句指定的变量对数据集排序。
例如，假设我们已经把class1数据集按性别排序，则下面PRINT 过程可以把男、女生分别列出：proc print data=class1 ; by sex;run;4．OUTPUT语句过程步中经常用OUTPUT语句指定输出结果存放的数据集。
不同过程中把输出结果存入数据集的方法各有不同，OUTPUT语句是使用频繁的语句之一。
其语法格式为：OUTPUT OUT=输出数据集名关键字=变量名关键字=变量名…;其中用OUT=给出了存放结果数据集的名字，关键字用于定义输出变量名，用“关键字=变量名”的方式指定了系统自动输出变量与存储变量之间的对应关系。
等号后面的变量名指定了输出数据集中的存储变量名称。
例如：proc means data=data_prg.class1; var math; output out=result02 n=n mean=meanmath var=varmath;run;proc print data=result02; run;在DATA步中也可以用FORMAT语句规定变量的输出格式，用LABEL 语句规定变量的标签，用LENGTH语句规定变量的存储长度，用ATTRIB语句同时规定变量的各属性。
用SAS的mixed过程拟合林分的线性差分生长模型
用SAS的mixed过程拟合林分的线性差分生长模型【摘要】本研究的目的在于研究如何用SAS的proc mixed过程拟合线性代数差分模型。
所用数据来源于148个集约经营火炬松人工林。
直接拟合了一个胸高断面积的收获模型，而非代数差分生长模型。
模型拟合过程如下：i）.同时确定随林分变化的参数和最优拟合的方差结构模型；ii）.依据AIC、BIC和极大似然比检验化简期望模型；iii）.用代数差分法将拟合的收获模型转化为代数差分生长模型。
【关键词】线性代数差分模型；mixed过程；模型筛选；林分生长与收获预估0.前言在林分生长与收获预估的模型中，差分生长模型得到了广泛的应用。
线性差分模型基本上为Schumacher模型的变型，广泛应用于林分蓄积、胸高断面积的建模，以及单位面积株数和优势木树高生长模型。
差分生长模型拟合方法有“直接最小二乘估计法”和“分类变量回归法”[1]。
一般认为后者可以获得近似无偏的估计，而前者则导致检验统计量如RMSE的失真[2]。
传统上差分生长模型的拟合主要是直接拟合差分生长模型，然后根据拟合统计量如RMSE、R2等确定最优拟合模型。
与传统方法不同，本文直接拟合生长模型，在获得参数估计值后，再用代数差分法导出相应的代数差分生长模型。
这样做的优越之处在于非常便于对期望模型和方差结构模型进行筛选。
更为重要的是，可以通过模型拟合识别最适合的随林分变化参数。
本文详细讨论了如何用“分类变量回归法”和SAS的mixed过程拟合代数差分生长模型，可简述如下：i）.直接以生长收获模型为对象，同时确定一个随林分变化的参数和最优拟合方差结构模型；ii）. 保持方差结构模型不变，根据拟合统计量逐步化简期望模型；iii）.在确定最优拟合的期望模型后，运用代数差分法导出相对应的代数差分生长模型。
所有拟合与筛选均用SAS的mixed过程完成，并给出了详细的SAS代码和代码解释。
1.方法与材料1.1数据数据来源于148个集约经营的火炬松实验人工林逐年观测的固定样地数据（样地约0.152公顷）。
20个SAS过程步
20个SAS过程步
1、PROC
MEANS--数据描述：计算均数、标准差、最大值、最小值、变量有效数据个数、变量缺失个数
2、PROC UNIV ARIATE--正态性检验
3、PROC TTEST--两独立样本检验
4、PROC NPAR1WAR--秩和检验
5、PROC ANOV A--方差分析
6、PROC CORR--相关性分析
7、PROC REG--回归分析
8、PROC FREQ--计数资料描述；卡方检验；诊断试验
9、PROC LOGISTIC--结局是二分类的Logisitc回归分析
10、PROC PHREG--生存分析
11、PROC POWER--样本量及把握度计算
12、PROC PRINT--显示数据集
13、PROC GLM--回归分析或协方差分析
14、PROC RANK--给某变量排次或按序分组
15、PROC SORT--按某变量排序
16、PROC SURVEYSELECT--概率抽样
17、PORC IMPORT--导入数据集
18、PROC EXPORT--导出数据集
19、PROC CONTENTS--产生一个数据集的头文件，包含了多种该数据集的信息
20、PROC TABULATE--输出报表。
SAS过程简介
第49章 SAS过程简介用编程法运行SAS，通常需要两步，第一步，叫SAS数据步，此步产生SAS数据集；第二步，叫SAS过程步，此步调用SAS软件包中真正的程序（称为SAS过程）处理提供的SAS 数据集。
本章将介绍以下主要内容：其一，SAS过程步的一般形式；其二，SAS/BASE模块中常用的一些过程及其主要功能；其三，SAS/STAT模块中常用的一些过程及其主要功能。
49.1 SAS过程步的一般形式SAS过程步的一般形式为：PROC 过程名 DATA=输入数据集 选项;过程语句 / 选项;过程语句 / 选项;……RUN;其中PROC是过程步开始的标志，在PROC后至少要留一个空格，紧随其后的是一个英文单词（如PRINT、SORT、…），该单词叫SAS过程名。
SAS软件中有很多模块（如SAS/BASE、SAS/STAT、SAS/GRAPH、…），每个模块中都有很多具体的SAS过程。
在PROC后写上一个具体的过程名，就是要求SAS系统调用该过程对给定的SAS数据集进行处理。
写在“PROC 过程名”之后的内容，都叫作PROC语句的选择项，简称PROC语句的选项。
所谓“选项”，就是根据用户的需要，可选可不选，用来规定过程运行的一些设置。
若某些选项没选，SAS系统就取隐含的或默认的或缺省的内容。
例如，当“DATA=输入数据集”未被选定时，SAS系统就使用在此之前最后生成的数据集为分析之用的数据集。
如果有多个选项，彼此之间需用空格分开。
每个SAS语句都以分号结束，而每个过程步一般以RUN 语句结束。
还有一种所谓“交互式过程”可以在遇到RUN语句时不结束过程运行，只有遇到QUIT语句或者下一个过程步、数据步时才结束。
在一个SAS过程步中，根据需要，可以写多个SAS过程步语句。
49.2 SAS/BASE模块中常用的一些过程及其主要功能49.2.1 CHART过程CHART过程可以产生垂直和水平直方图、块形图、饼图和星形图。
proc mixed 误差项 sas 混合模型 公式
proc mixed 误差项sas 混合模型公式全文共四篇示例，供读者参考第一篇示例：PROC MIXED是SAS中用于混合模型分析的过程，混合模型是一种能够处理多层次结构或者重复测量数据的统计模型。
在混合模型中，我们可以同时考虑固定效应和随机效应，进而对不同层次的变量进行分析。
在混合模型中，误差项扮演着非常重要的角色，它是模型中必不可少的一个组成部分。
本文将介绍关于PROC MIXED中误差项的相关知识，并给出相应的混合模型公式。
误差项在混合模型中是指未被模型中的自变量所解释的部分，也就是模型中未被考虑的随机误差。
在混合模型中，我们通常假设误差项服从正态分布，并且具有均值为0、方差为σ^2的特性。
误差项的存在使得我们能够量化模型中的不确定性，评估模型的拟合程度，并且进行相关的统计推断。
在PROC MIXED中，我们可以通过指定各种固定效应和随机效应来构建混合模型。
常见的混合模型可以被表达为如下的公式：Y = Xβ + Zγ + εY表示观测到的因变量向量，X是固定效应矩阵，β是固定效应参数向量，Z是随机效应矩阵，γ是随机效应参数向量，ε是误差项向量。
在该公式中，固定效应表示各个因素对因变量的整体影响，而随机效应则表示了在样本中的个体差异。
误差项则是模型中未被解释的残差部分。
在具体的数据分析过程中，我们需要根据研究的实际情况来构建混合模型。
在进行实验设计时，我们需要考虑实验中的重复测量数据或者样本数据的层次结构。
在这种情况下，混合模型能够更好地分析不同层次之间的关系，并且考虑到各个层次的变异性。
通过PROC MIXED进行混合模型分析时，我们可以通过设定不同的协方差结构来进一步扩展模型的适用范围。
可以选择不同的协方差结构来描述不同层次的数据之间的相关性。
PROC MIXED还提供了丰富的选项来进行模型拟合和参数估计，包括最大似然估计、重复测量设计、协变量调整等功能。
第二篇示例：混合模型是一种在统计分析中常用的模型，特别是当研究对象存在多个层次或重复测量时。
SAS分析常用的过程过程步大全
SAS分析常用的过程过程步大全为区分过程名称的拼写，故意部分小写，以便识别和记忆。
基本SAS程序代码结构：---------PROC MODE data=Arndata.moddat; /* 命令的解释*/var y x1-x6; /* 命令的解释 */model y = x1-x6;run;------------------------------------------正态性检验PROC UNIvariate---------PROCUNIvariate data=Arndata.unidat;var x1;run;------------------------------------------相关分析和回归分析PROC REG 回归---------PROC REG data=Arndata.regdat;var y x1-x6;model y = x1-x6 / selection=stepwise;/* 加入逐步回归选项 */print cli; /* 加入输出预测结果部分，还可以输出acov,all,cli,clm,collin,collinoint,cookd,corrb,covb,dw(时序检验统计量),i,influence,p,partial,pcorr1,pcorr2,r,scorr1,scorr2,seqb,spec,ss1,ss2,stb,tol, vif(异方差检验统计量),xpx*/plot y*x2 / conf95; /* 做散点图 */run;---------------------------------------------------DATA Arndata.regdat;x2x2 = x2*x2;x1x2 = x1*x2;PROC REG data=Arndata.regdat;var y x1 x2 x2x2 x1x2 ; /* 多项式回归,非线性回归 */model y = x1 x2 x2x2 x1x2 / selection=stepwise; /* 加入逐步回归选项*/print cli;plot y*x2 / conf95; /* 做散点图 */run;------------------------------------------PROC RSreg 二次响应面回归PROC ORTHOreg 病态数据回归PROC NLIN 非线性回归PROC TRANSreg 变换回归PROC CALIS 线性结构方程和路径分析PROC GLM 一般线性模型PROC GENmod 广义线性模型方差分析PROC ANOVA 单因素均衡数据和非均衡数据---------PROC ANOVA data=Arndata.anovadat; /* 命令的解释 */class typ; /* 命令的解释 */model y = typ; /* 可以看出此处是单因素方差分析(分类型自变量对数值型自变量的影响) */run;------------------------------------------PROC GLM 多因素非均衡数据:---------PROC GLM data=Arndata.glmdat; /* 命令的解释*/class typea typeb; /* 命令的解释 */model y = typea typeb; /* 可以看出此处是不考虑交互作用的多因素方差分析(分类型自变量对数值型自变量的影响) */run;---------------------------------------------------PROC GLM data=Arndata.glmdat; /* 命令的解释*/class typea typeb; /* 命令的解释 */model y = typea typeb typea*typeb; /* 可以看出此处是考虑交互作用的多因素方差分析(分类型自变量对数值型自变量的影响) */run;------------------------------------------主成分分析PROC PRINcomp---------PROCPRINcomp data=Arndata.pmdat n=4 out=w1 outstat=w2 ;var x1-x6;PROC print data=w1;PROC plot data=w1 vpct=80; /* 一句话，其实print就是plot输出图形的文字形式而已 */plot prin1*prin2 $ districts='*'/haxis=-3.5 to 3 by 0.5 HREF=-2,0,2vaxis=-3 to 4.5 by 1.5 HREF=-2,0,2; /* 主成分的散点图，也就是载荷图 */run;------------------------------------------因子分析PROC FACTOR---------PROC FACTOR data=Arndata.factordat simple corr ;var y x1-x6;title'18个财务指标的分析';title2'主成分解';run;PROC FACTOR data=Arndata.factordatn=4 ; /* 选择4个公共因子 */ var y x1-x6;run;PROC FACTOR data=Arndata.factordat n=4rotate=VARImaxREorder; /* 因子旋转：方差最大因子法 */var y x1-x6;run;------------------------------------------PROC SCORE---------PROC FACTOR data=Arndata.factordat n=4rotate=VARImax REorder score out=score_Out; /* 输出因子得分矩阵 */run;PROC print data=score_Out;var districts factor1 factor2 factor3 factor4;run;PROC plot data=score_Out;plot factor1*factor2 $ districts='*' / href=0 Vref=0; /* 因子的散点图，也就是载荷图 */run;------------------------------------------典型相关分析PROC CANcorr基本SAS程序代码结构：---------DATAjt(TYPE=CORR); /*TYPE=CORR 表明数据类型为相关矩阵，而不是原始数据, type还可以是cov,ucov,factor,sscp,ucorr等*/input names$ 1-2(x1 x2 y1-y3)(6.); /* name $ 表示读取左侧的变量名，1-2表示变量名的字符落在第1,2列上 */cards;x1 1 0.8 ……x2 ……y1 ……y2 ……y3 ……;PROC CANcorrdata=Arndata.cancorrdatedf=70 redundancy; /* 误差自由度的参考值，默认值是n=1000；redundancy表示输出冗余度分析的结果 */var x1 x2;with y1 y2 y3;run;------------------------------------------对应分析 /* 交叉表分析的拓展，寻找行和列的关系，一般行指代各种cases，而列代表各种visions */PROC CORResp---------PROC CORRespdata=Arndata.correspdat out=result;var x1-x6;id Type;run;options ps=40;proc plot data=result;plot dim2*dim1="*" $ Type / boxhaxis=-0.2 to 0.3 by 0.1Vaxis=-0.1 to 0.3 by 0.1Href=0 Vref=0;run;------------------------------------------聚类分析PROC CLUSTER---------PROC CLUSTER data=Arndata.clusdatmethod=ave outtree=clusdat_Out;var x1-x6;id datid;run;proc tree horizontal; /* 做聚类树 */run;------------------------------------------PROC FASTclus---------PROC FASTclus data=Arndata.clusdatmaxclusters=3 list out=clusdat_Out;var x1-x6;id datid;run;------------------------------------------PROC ACEclusPROC VARCLUS---------PROC VARclus data=Arndata.clusdat;/* 系统默认使用主成分法聚类 */var x1-x6;run;---------PROC VARclus hierarchy data=Arndata.clusdat; /* 保证分析过程中不同水平的谱系结构 */var x1-x6;run;---------PROC VARclus centroid data=Arndata.clusdatouttree=clusdat_out; /* 使用重心法聚类 */ var x1-x6;run;------------------------------------------PROC TREE---------PROC TREE data=Arndata.clusdat horizontal; /* 使用TREE过程绘制聚类谱系图*/var x1-x6;run;------------------------------------------判别分析PROC DISCRIM---------PROC DISCRIM data=Arndata.discrimdatlist out=discrimdat_Out distance pool=yes;class Typ; /* 指定分类变量 */var x1-x6; /* 用于建立判别识别函数的变量 */id iddiscrim; /* 标注样本的变量 */run;---------第二种方法，将需要判别的新样本放在testdata里：---------PROC DISCRIM data=Arndata.discrimdat1testdata=Arndata.discrimdat2testlist testout=discrimdat_Out; /* 将原来的几个选项加注test标示 */class Typ; /* 指定分类变量 */var x1-x6; /* 用于建立判别识别函数的变量 */id iddiscrim; /* 标注样本的变量 */run;------------------------------------------PROC STEPdisc：逐步判别分析过程---------PROC STEPdisc method=stepwise data=Arndata.discrimdatSLentry=0.10 SLstay=0.10; /* 设定引入和剔除的显著性水平 */class Typ; /* 指定分类变量 */var x1-x6; /* 用于建立判别识别函数的变量 */run;------------------------------------------PROC CANdisc： Fisher判别分析过程---------PROC CANdiscdata=Arndata.discrimdatout=discrimdat_Outdistance simple;class Typ; /* 指定分类变量 */var x1-x6; /* 用于建立判别识别函数的变量 */run;proc print data=discrimdat_Out;run;-----------------------------------------------------------------------------------------------------------------------------------------------------------友情协助：特征库豆瓣统计学小组 /group/stats。
第21章 SAS过程步操作基础
means过程可计算的统计量（一）
关键字
N NMISS MEAN STD STDERR VAR MEDIAN CV
所代表的含义
有效数据记录数 缺失数据记录数 均数 标准差 标准误 方差 中位数 变异系数
关键字
MAX MIN RANGE SUM SUMWGT CSS USS CLM
所代表的含义
最大值 最小值 全距 总计 加权总计 校正的离均差平方和 未校正的离均差平方和 可信限（上、下界值）
contents过程
contents过程用于显示指定的SAS数据集的有关信息 或者相应逻辑库中所包含成员的列表信息。 对于指定的SAS数据集，contents过程将列出数据集 的各种属性信息，以及所包含的全部变量及其属性。 有关变量信息的列表将按照字母顺序排列，变量属性 信息包括变量类型、长度、标签以及格式等。 contents过程的一般形式如下： proc contents data=SAS-data-set options; run;
means过程示例
data test;
do i=1 to 3; do j=1 to 2; do k=1 to 30; x=abs(ranuni(0))*10+8;
y=x**1.5;
output; end; end; end;
run;
proc means data=test mean median std var cv t probt; class i j; var x y; output out=outdata mean(x y)=mx my std(x y)=sx xy; run;
print过程支持的其它语句
proc mixed 置信区间
proc mixed 置信区间一、介绍proc mixed 是SAS 软件中的一个过程，用于拟合混合线性模型。
在统计分析中，经常需要对模型参数进行置信区间估计，以评估变量之间的关系是否显著。
本文将介绍如何使用proc mixed 进行置信区间估计，并解释置信区间的含义和解读方法。
二、置信区间的概念置信区间是对参数估计的不确定性进行度量的一种方法。
在回归分析中，我们通常对模型中的系数进行估计，例如斜率和截距。
通过计算置信区间，我们可以得到一个区间，该区间内的真实参数值有一定的概率落在其中。
置信区间的计算基于样本数据和统计理论，其中最常用的方法是基于正态分布的置信区间。
在proc mixed 中，默认使用的是95%的置信区间，即我们希望真实参数值在计算出的区间内的概率为95%。
三、使用 proc mixed 进行置信区间估计使用 proc mixed 进行置信区间估计的步骤如下：1. 导入数据：首先需要将数据导入SAS 软件中，可以使用data step 或者 proc import 进行数据导入。
2. 定义模型：使用proc mixed 过程，通过指定固定效应和随机效应来定义混合线性模型。
例如，可以使用类别变量作为固定效应，使用随机效应来建模不同个体之间的差异。
3. 估计参数：使用proc mixed 进行模型的拟合和参数估计。
拟合过程将生成各个模型参数的估计值。
4. 计算置信区间：使用estimate 语句在proc mixed 中计算置信区间。
可以通过指定 alpha 参数来控制置信水平，默认为0.05。
5. 解读结果：根据计算得到的置信区间，可以判断模型中的变量之间是否存在显著差异。
如果置信区间包含零，则说明差异不显著；如果置信区间不包含零，则说明差异显著。
四、置信区间的解读置信区间提供了一种度量参数估计的不确定性的方法。
通常情况下，我们希望置信区间越窄越好，因为窄的置信区间意味着对参数估计的确定性更高。
SAS过程步操作基础
推断性统计分析
01
推断性统计分析
通过样本数据推断总体特征，对 总体参数进行估计和检验，从而 对总体做出科学推断。
02
推断性统计分析的 步骤
1.确定研究问题；2.选择合适的 统计方法；3.收集样本数据；4. 进行统计分析；5.结果解释和推 断。
03
推断性统计分析的 常用方法
t检验、方差分析、回归分析、卡 方检验等。
01
文本格式
如CSV、TXT等，适合于与其他软件 或系统进行数据交换。
电子表格格式
如Excel、OpenOffice等，适合于数 据分析与可视化。Biblioteka 0302数据库格式
如SQL、Access等，适合于存储在 数据库中。
统计报告格式
如PDF、DOC等，适合于生成统计 报告或文档。
04
数据保存路径选择
本地存储
SAS过程步的分类
总结词
SAS过程步可以根据其功能和应用场景分为多种类型 。
详细描述
根据其功能和应用场景，SAS过程步可以分为多种类型， 如数据输入/输出过程步（如`INPUT`和`OUTPUT`）、 数据转换过程步（如`IF`、`WHERE`、`SET`等）、数据 筛选过程步（如`WHERE`）、数据分组和汇总过程步 （如`GROUP BY`、`SUM`等）、数据标签和格式化过 程步（如`LABEL`、`FORMAT`）等。这些过程步在数据 处理过程中起着不同的作用，能够完成各种复杂的数据 处理任务。
THANKS
SAS过程步操作基础
目录
Contents
• SAS过程步概述 • 数据输入与处理 • 数据分析与可视化 • 数据输出与保存 • SAS过程步进阶操作
01 SAS过程步概述
SAS_PROC_MIXED
SAS PROC MIXED 1SAS PROC MIXEDhttp://www.id.unizh.ch/software/unix/statmath/sas/sasdoc/stat/chap41/index.htmOverviewThe MIXED procedure fits a variety of mixed linear models to data and enables you to use these fitted models to make statistical inferences about the data. A mixed linear model is a generalization of the standard linear model used in the GLM procedure, the generalization being that the data are permitted to exhibit correlation and nonconstant variability. The mixed linear model, therefore, provides you with the flexibility of modeling not only the means of your data (as in the standard linear model) but their variances and covariances as well. The primary assumptions underlying the analyses performed by PROC MIXED are as follows: • • • The data are normally distributed (Gaussian). The means (expected values) of the data are linear in terms of a certain set of parameters. The variances and covariances of the data are in terms of a different set of parameters, and they exhibit a structure matching one of those available in PROC MIXED.Since Gaussian data can be modeled entirely in terms of their means and variances/covariances, the two sets of parameters in a mixed linear model actually specify the complete probability distribution of the data. The parameters of the mean model are referred to as fixed-effects parameters, and the parameters of the variance-covariance model are referred to as covariance parameters. The fixed-effects parameters are associated with known explanatory variables, as in the standard linear model. These variables can be either qualitative (as in the traditional analysis of variance) or quantitative (as in standard linear regression). However, the covariance parameters are what distinguishes the mixed linear model from the standard linear model. The need for covariance parameters arises quite frequently in applications, the following being the two most typical scenarios: • • The experimental units on which the data are measured can be grouped into clusters, and the data from a common cluster are correlated. Repeated measurements are taken on the same experimental unit, and these repeated measurements are correlated or exhibit variability that changes.The first scenario can be generalized to include one set of clusters nested within another. For example, if students are the experimental unit, they can be clustered into classes, which in turn can be clustered into schools. Each level of this hierarchy can introduce an additional source of variability and correlation. The second scenario occurs in longitudinal studies, where repeated measurements are taken over time. Alternatively, the repeated measures could be spatial or multivariate in nature. PROC MIXED provides a variety of covariance structures to handle the previous two scenarios. The most common of these structures arises from the use of random-effects parameters, which are additional unknown random variables assumed to impact the variability of the data. The variances of the random-effects parameters, commonly known as variance components, become the covariance parameters for this particular structure. Traditional mixed linear models contain both fixed- and random-effects parameters, and, in fact, it is the combination of these two types of effects that led to the name mixed model. PROC MIXED fits not only these traditional variance component models but numerous other covariance structures as well. PROC MIXED fits the structure you select to the data using the method of restricted maximum likelihood (REML), also known as residual maximum likelihood. It is here that the Gaussian assumption for the data is exploited. OtherSAS PROC MIXED 2estimation methods are also available, including maximum likelihood and MIVQUE0. The details behind these estimation methods are discussed in subsequent sections. Once a model has been fit to your data, you can use it to draw statistical inferences via both the fixed-effects and covariance parameters. PROC MIXED computes several different statistics suitable for generating hypothesis tests and confidence intervals. The validity of these statistics depends upon the mean and variance-covariance model you select, so it is important to choose the model carefully. Some of the output from PROC MIXED helps you assess your model and compare it with others.Basic FeaturesPROC MIXED provides easy accessibility to numerous mixed linear models that are useful in many common statistical analyses. In the style of the GLM procedure, PROC MIXED fits the specified mixed linear model and produces appropriate statistics. Some basic features of PROC MIXED are • • • • • • • covariance structures, including variance components, compound symmetry, unstructured, AR(1), Toeplitz, spatial, general linear, and factor analytic GLM-type grammar, using MODEL, RANDOM, and REPEATED statements for model specification and CONTRAST, ESTIMATE, and LSMEANS statements for inferences appropriate standard errors for all specified estimable linear combinations of fixed and random effects, and corresponding t- and F-tests subject and group effects that enable blocking and heterogeneity, respectively REML and ML estimation methods implemented with a Newton-Raphson algorithm capacity to handle unbalanced data ability to create a SAS data set corresponding to any tablePROC MIXED uses the Output Delivery System (ODS), a SAS subsystem that provides capabilities for displaying and controlling the output from SAS procedures. ODS enables you to convert any of the output from PROC MIXED into a SAS data set. See the "Changes in Output" section.Notation for the Mixed ModelThis section introduces the mathematical notation used throughout this chapter to describe the mixed linear model. You should be familiar with basic matrix algebra (refer to Searle 1982). A more detailed description of the mixed model is contained in the "Mixed Models Theory" section. A statistical model is a mathematical description of how data are generated. The standard linear model, as used by the GLM procedure, is one of the most common statistical models:In this expression, y represents a vector of observed data, known design matrix X, andis an unknown vector of fixed-effects parameters with . Theis an unknown random error vector modeling the statistical noise aroundSAS PROC MIXED 3focus of the standard linear model is to model the mean of y by using the fixed-effects parameters . The residual errors are assumed to be independent and identically distributed Gaussian random variables with mean 0 and variance .The mixed model generalizes the standard linear model as follows:Here, is an unknown vector of random-effects parameters with known design matrix Z, and is an unknown random error vector whose elements are no longer required to be independent and homogeneous.To further develop this notion of variance modeling, assume that and are Gaussian random variables that are uncorrelated and have expectations 0 and variances G and R, respectively. The variance of y is thus V = ZGZ' + R Note that, when and Z = 0, the mixed model reduces to the standard linear model.You can model the variance of the data, y, by specifying the structure (or form) of Z, G, and R. The model matrix Z is set up in the same fashion as X, the model matrix for the fixed-effects parameters. For G and R, you must select some covariance structure. Possible covariance structures include • • • • • • • variance components compound symmetry (common covariance plus diagonal) unstructured (general covariance) autoregressive spatial general linear factor analyticBy appropriately defining the model matrices X and Z, as well as the covariance structure matrices G and R, you can perform numerous mixed model analyses.PROC MIXED Contrasted with Other SAS ProceduresPROC MIXED is a generalization of the GLM procedure in the sense that PROC GLM fits standard linear models, and PROC MIXED fits the wider class of mixed linear models. Both procedures have similar CLASS, MODEL, CONTRAST, ESTIMATE, and LSMEANS statements, but their RANDOM and REPEATED statements differ (see the following paragraphs). Both procedures use the nonfull-rank model parameterization, although the sorting of classification levels can differ between the two. PROC MIXED computes only Type I -Type III tests of fixed effects, while PROC GLM offers Types I - IV. The RANDOM statement in PROC MIXED incorporates random effects constituting the vector in the mixed model. However, in PROC GLM, effects specified in the RANDOM statement are still treated as fixed as far as the model fit is concerned, and they serve only to produce correspondingSAS PROC MIXED 4expected mean squares. These expected mean squares lead to the traditional ANOVA estimates of variance components. PROC MIXED computes REML and ML estimates of variance parameters, which are generally preferred to the ANOVA estimates (Searle 1988; Harville 1988; Searle, Casella, and McCulloch 1992). Optionally, PROC MIXED also computes MIVQUE0 estimates, which are similar to ANOVA estimates. The REPEATED statement in PROC MIXED is used to specify covariance structures for repeated measurements on subjects, while the REPEATED statement in PROC GLM is used to specify various transformations with which to conduct the traditional univariate or multivariate tests. In repeated measures situations, the mixed model approach used in PROC MIXED is more flexible and more widely applicable than either the univariate or multivariate approaches. In particular, the mixed model approach provides a larger class of covariance structures and a better mechanism for handling missing values (Wolfinger and Chang 1995). PROC MIXED subsumes the VARCOMP procedure. PROC MIXED provides a wide variety of covariance structures, while PROC VARCOMP estimates only simple random effects. PROC MIXED carries out several analyses that are absent in PROC VARCOMP, including the estimation and testing of linear combinations of fixed and random effects. The ARIMA and AUTOREG procedures provide more time series structures than PROC MIXED, although they do not fit variance component models. The CALIS procedure fits general covariance matrices, but it does not allow fixed effects as does PROC MIXED. The LATTICE and NESTED procedures fit special types of mixed linear models that can also be handled in PROC MIXED, although PROC MIXED may run slower because of its more general algorithm. The TSCSREG procedure analyzes time-series cross-sectional data, and it fits some structures not available in PROC MIXED.SyntaxThe following statements are available in PROC MIXED. PROC MIXED < options > ; BY variables ; CLASS variables ; ID variables ; MODEL dependent = < fixed-effects > < / options > ; RANDOM random-effects < / options > ; REPEATED < repeated-effect > < / options > ; PARMS (value-list) ... < / options > ; PRIOR < distribution > < / options > ; CONTRAST 'label' < fixed-effect values ... > < | random-effect values ... > , ... < / options > ; ESTIMATE 'label' < fixed-effect values ... > < | random-effect values ... >< / options > ; LSMEANS fixed-effects < / options > ; MAKE 'table' OUT=SAS-data-set ; WEIGHT variable ; Items within angle brackets ( < > ) are optional. The CONTRAST, ESTIMATE, LSMEANS, MAKE, and RANDOM statements can appear multiple times; all other statements can appear only once. The PROC MIXED and MODEL statements are required, and the MODEL statement must appear after the CLASS statement if a CLASS statement is included. The CONTRAST, ESTIMATE, LSMEANS, RANDOM, and REPEATED statements must follow the MODEL statement. The CONTRAST and ESTIMATE statements must also follow any RANDOM statements.SAS PROC MIXED 5Table 41.1 summarizes the basic functions and important options of each PROC MIXED statement. The syntax of each statement in Table 41.1 is described in the following sections in alphabetical order after the description of the PROC MIXED statement. Table 41.1: Summary of PROC MIXED Statements Statement PROC MIXED BY Description invokes the procedure performs multiple PROC MIXED analyses in one invocation declares qualitative variables that create indicator variables in design matrices lists additional variables to be included in predicted values tables Important Options DATA= specifies input data set, METHOD= specifies estimation method noneCLASSnoneIDnoneMODELspecifies dependent variable S requests solution for fixed-effects parameters, DDFM= specifies and fixed effects, setting up X denominator degrees of freedom method, OUTP= outputs predicted values to a data set specifies random effects, setting up Z and G sets up R SUBJECT= creates block-diagonality, TYPE= specifies covariance structure, S requests solution for random-effects parameters, G displays estimated G SUBJECT= creates block-diagonality, TYPE= specifies covariance structure, R displays estimated blocks of R, GROUP= enables between-subject heterogeneity, LOCAL adds a diagonal matrix to R HOLD= and NOITER hold the covariance parameters or their ratios constant, PDATA= reads the initial values from a SAS data set NSAMPLE= specifies the sample size, SEED= specifies the starting seed E displays the L matrix coefficients CL produces confidence limits DIFF computes differences of the least squares means, ADJUST= performs multiple comparisons adjustments, AT changes covariates, OM changes weighting, CL produces confidence limits, SLICE= tests simple effects none. Has been superceded by the Output Delivery System (ODS) noneRANDOMREPEATEDPARMSspecifies a grid of initial values for the covariance parameters performs a sampling-based Bayesian analysis for variance component models constructs custom hypothesis tests constructs custom scalar estimates computes least squares means for classification fixed effectsPRIORCONTRAST ESTIMATE LSMEANSMAKE WEIGHTconverts any displayed table into a SAS data set specifies a variable by which to weight RSAS PROC MIXED 6PROC MIXED StatementPROC MIXED < options >; The PROC MIXED statement invokes the procedure. You can specify the following options. ABSOLUTE makes the convergence criterion absolute. By default, it is relative (divided by the current objective function value). See the CONVF, CONVG, and CONVH options in this section for a description of various convergence criteria. ALPHA=number requests that confidence limits be constructed for the covariance parameter estimates with confidence level 1-number. The value of number must be between 0 and 1; the default is 0.05. ASYCORR produces the asymptotic correlation matrix of the covariance parameter estimates. It is computed from the corresponding asymptotic covariance matrix (see the description of the ASYCOV option, which follows). For ODS purposes, the label of the "Asymptotic Correlation" table is "AsyCorr." ASYCOV requests that the asymptotic covariance matrix of the covariance parameters be displayed. By default, this matrix is the observed inverse Fisher information matrix, which equals 2H-1, where H is the Hessian (second derivative) matrix of the objective function. See the "Covariance Parameter Estimates" section for more information about this matrix. When you use the SCORING= option and PROC MIXED converges without stopping the scoring algorithm, PROC MIXED uses the expected Hessian matrix to compute the covariance matrix instead of the observed Hessian. For ODS purposes, the label of the "Asymptotic Covariance" table is "AsyCov." CL<=WALD> requests confidence limits for the covariance parameter estimates. A Satterthwaite approximation is used to construct limits for all parameters that have a default lower boundary constraint of zero. These limits take the formwhere , Z is the Wald statistic , and the denominators are quantiles of the distribution with degrees of freedom. Refer to Milliken and Johnson (1992) and Burdick and Graybill (1992) for similar techniques. For all other parameters, Wald Z-scores and normal quantiles are used to construct the limits. The optional =WALD specification requests Wald limits for all parameters. The confidence limits are displayed as extra columns in the "Covariance Parameter Estimates" table. The confidence level is by default; this can be changed with the ALPHA= option.CONVF<=number> requests the relative function convergence criterion with tolerance number. The relative function convergence criterion isSAS PROC MIXED 7where fk is the value of the objective function at iteration k. To prevent the division by |fk|, use the ABSOLUTE option. The default convergence criterion is CONVH, and the default tolerance is 1E-8. CONVG <=number> requests the relative gradient convergence criterion with tolerance number. The relative gradient convergence criterion iswhere fk is the value of the objective function, and gjk is the jth element of the gradient (first derivative) of the objective function, both at iteration k. To prevent division by |fk|, use the ABSOLUTE option. The default convergence criterion is CONVH, and the default tolerance is 1E-8. CONVH<=number> requests the relative Hessian convergence criterion with tolerance number. The relative Hessian convergence criterion iswhere fk is the value of the objective function, gk is the gradient (first derivative) of the objective function, and Hk is the Hessian (second derivative) of the objective function, all at iteration k. If Hk is singular, then PROC MIXED uses the following relative criterion:To prevent the division by |fk|, use the ABSOLUTE option. The default convergence criterion is CONVH, and the default tolerance is 1E-8. COVTEST produces asymptotic standard errors and Wald Z-tests for the covariance parameter estimates.SAS PROC MIXED 8DATA=SAS-data-set names the SAS data set to be used by PROC MIXED. The default is the most recently created data set. DFBW has the same effect as the DDFM=BW option in the MODEL statement. EMPIRICAL computes the estimated variance-covariance matrix of the fixed-effects parameters by using the asymptotically consistent estimator described in Huber (1967), White (1980), Liang and Zeger (1986), and Diggle, Liang, and Zeger (1994). This estimator is commonly referred to as the "sandwich" estimator, and it is computed as follows:Here, , S is the number of subjects, and matrices with an i subscript are those for the ith subject. You must include the SUBJECT= option in either a RANDOM or REPEATED statement for this option to take effect. When you specify the EMPIRICAL option, PROC MIXED adjusts all standard errors and test statistics involving the fixed-effects parameters. This changes output in the following tables (listed in Table 41.7): Contrast, CorrB, CovB, Diffs, Estimates, InvCovB, LSMeans, MMEq, MMEqSol, Slices, SolutionF, Tests1 -Tests3. The OUTP= and OUTPM= data sets are also affected. Finally, the Satterthwaite and Kenward-Roger degrees of freedom methods are not available if you specify EMPIRICAL. IC displays a table of various information criteria. Four different criteria are computed in four different ways, producing 16 values in all. Table 41.2 displays the four criteria in both larger-is-better and smaller-is-better forms. Table 41.2: Information Criteria Criteria Larger-is-better Smaller-is-better Reference AIC l- d HQIC l- d loglogn BIC l- d/2 logn CAIC l- d(logn + 1)/2 -2l+ 2d -2l+ 2d loglogn -2l+ d logn -2l+ d(logn + 1) Akaike (1974) Hannan and Quinn (1979) Schwarz (1978) Bozdogan (1987)Here l denotes the maximum value of the (possibly restricted) log likelihood, d the dimension of the model, and n the number of effective observations. In Version 6 of SAS/STAT software, n equals the number of valid observations for maximum likelihood estimation and n-p for restricted maximum likelihood estimation, where p equals the rank of X. In later versions, n equals the number of effective subjects as displayed in the "Dimensions" table, unless this value equals 1, in which case n reverts to the Version 6 values. PROC MIXED evaluates the criteria for both forms using d equal to both q and q+p, where q is theSAS PROC MIXED 9effective number of estimated covariance parameters. In Version 6, when a parameter estimate lies on a boundary constraint, then it is still included in the calculation of d, but in later versions it is not. The most common example of this behavior is when a variance component is estimated to equal zero. For ODS purposes, the name of the "Information Criteria" table is "InfoCrit." INFO is a default option. The creation of the "Model Information" and "Dimensions" tables can be suppressed using the NOINFO option. Note that, in Version 6, this option displays the "Model Information" and "Dimensions" tables. ITDETAILS displays the parameter values at each iteration and enables the writing of notes to the SAS log pertaining to "infinite likelihood" and "singularities" during Newton-Raphson iterations. LOGNOTE writes periodic notes to the log describing the current status of computations. It is designed for use with analyses requiring extensive CPU resources. MAXFUNC=number specifies the maximum number of likelihood evaluations in the optimization process. The default is 150. MAXITER=number specifies the maximum number of iterations. The default is 50. METHOD=REML METHOD=ML METHOD=MIVQUE0 METHOD=TYPE1 METHOD=TYPE2 METHOD=TYPE3 specifies the estimation method for the covariance parameters. The REML specification performs residual (restricted) maximum likelihood, and it is the default method. The ML specification performs maximum likelihood, and the MIVQUE0 specification performs minimum variance quadratic unbiased estimation of the covariance parameters. The METHOD=TYPEn specifications apply only to variance component models with no SUBJECT= effects and no REPEATED statement. An analysis of variance table is included in the output, and the expected mean squares are used to estimate the variance components (refer to Chapter 30, "The GLM Procedure," for further explanation). The resulting method-of-moment variance component estimates are used in subsequent calculations, including standard errors computed from ESTIMATE and LSMEANS statements. For ODS purposes, the new table names are "Type1," "Type2," and "Type3," respectively. MMEQ requests that coefficients of the mixed model equations be displayed. These areassuming thatis nonsingular. Ifis singular, PROC MIXED produces the following coefficientsSAS PROC MIXED 10See the "Estimating and in the Mixed Model" section for further information on these equations. MMEQSOL requests that a solution to the mixed model equations be produced, as well as the inverted coefficients matrix. Formulas for these equations are provided in the preceding description of the MMEQ option. When is singular, and a generalized inverse of the left-hand-side coefficient matrix are transformed is a generalized inverse of the left-hand-sideto produce and , respectively, where using coefficient matrix of the original equations.NAMELEN<=number> specifies the length to which long effect names are shortened. The default and minimum value is 20. NOBOUND has the same effect as the NOBOUND option in the PARMS statement. NOCLPRINT<=number> suppresses the display of the "Class Level Information" table if you do not specify number. If you do specify number, only levels with totals that are less than number are listed in the table. NOINFO suppresses the display of the "Model Information" and "Dimensions" tables. NOITPRINT suppresses the display of the "Iteration History" table. NOPROFILE includes the residual variance as part of the Newton-Raphson iterations. This option applies only to models that have a residual variance parameter. By default, this parameter is profiled out of the likelihood calculations, except when you have specified the HOLD= or NOITER option in the PARMS statement. ORD displays ordinates of the relevant distribution in addition to p-values. The ordinate can be viewed as an approximate odds ratio of hypothesis probabilities. ORDER=DATA ORDER=FORMATTED ORDER=FREQ ORDER=INTERNAL specifies the sorting order for the levels of all CLASS variables. This ordering determines which parameters in the model correspond to each level in the data, so the ORDER= option may be useful when you use CONTRAST or ESTIMATE statements. The default is ORDER=FORMATTED, and its behavior has been modified for Version 8. Now, for numeric variables for which you have supplied no explicit format (that is, for which there is noSAS PROC MIXED 11corresponding FORMAT statement in the current PROC MIXED run or in the DATA step that created the data set), the levels are ordered by their internal (numeric) value. In releases previous to Version 8, numeric class levels with no explicit format were ordered by their BEST12. formatted values. In order to revert to the previous method you can specify this format explicitly for the CLASS variables. The change was implemented because the former default behavior for ORDER=FORMATTED often resulted in levels not being ordered numerically and required you to use an explicit format or ORDER=INTERNAL to get the more natural ordering. The following table shows how PROC MIXED interprets values of the ORDER= option. Value of ORDER= Levels Sorted By DATA FORMATTED order of appearance in the input data set external formatted value, except for numeric variables with no explicit format, which are sorted by their unformatted (internal) value FREQ descending frequency count; levels with the most observations come first in the order INTERNAL unformatted valueFor FORMATTED and INTERNAL, the sort order is machine dependent. For more information on sorting order, see the chapter on the SORT procedure in the SAS Procedures Guide and the discussion of BYgroup processing in SAS Language Reference: Concepts. RATIO produces the ratio of the covariance parameter estimates to the estimate of the residual variance when the latter exists in the model. RIDGE=number specifies the starting value for the minimum ridge value used in the Newton-Raphson algorithm. The default is 0.3125. SCORING<=number> requests that Fisher scoring be used in association with the estimation method up to iteration number, which is 0 by default. When you use the SCORING= option and PROC MIXED converges without stopping the scoring algorithm, PROC MIXED uses the expected Hessian matrix to compute approximate standard errors for the covariance parameters instead of the observed Hessian. The output from the ASYCOV and ASYCORR options is similarly adjusted. SIGITER is an alias for the NOPROFILE option. UPDATE is an alias for the LOGNOTE option.BY StatementBY variables ;SAS PROC MIXED 12You can specify a BY statement with PROC MIXED to obtain separate analyses on observations in groups defined by the BY variables. When a BY statement appears, the procedure expects the input data set to be sorted in order of the BY variables. The variables are one or more variables in the input data set. If your input data set is not sorted in ascending order, use one of the following alternatives: • • Sort the data using the SORT procedure with a similar BY statement. Specify the BY statement options NOTSORTED or DESCENDING in the BY statement for the MIXED procedure. The NOTSORTED option does not mean that the data are unsorted but rather means that the data are arranged in groups (according to values of the BY variables) and that these groups are not necessarily in alphabetical or increasing numeric order. Create an index on the BY variables using the DATASETS procedure (in base SAS software).•Since sorting the data changes the order in which PROC MIXED reads observations, the sorting order for the levels of the CLASS variable may be affected if you have specified ORDER=DATA in the PROC MIXED statement. This, in turn, affects specifications in the CONTRAST statements. For more information on the BY statement, refer to the discussion in SAS Language Reference: Concepts. For more information on the DATASETS procedure, refer to the discussion in the SAS Procedures Guide.CLASS StatementCLASS variables ;The CLASS statement names the classification variables to be used in the analysis. If the CLASS statement is used, it must appear before the MODEL statement. Classification variables can be either character or numeric. The procedure uses only the first 16 characters of a character variable. Class levels are determined from the formatted values of the CLASS variables. Thus, you can use formats to group values into levels. Refer to the discussion of the FORMAT procedure in the SAS Procedures Guide and to the discussions of the FORMAT statement and SAS formats in SAS Language Reference: Dictionary. You can adjust the display order of CLASS variable levels with the ORDER= option in the PROC MIXED statement.CONTRAST StatementCONTRAST 'label' < fixed-effect values ...> < | random-effect values ...> , ...< / options > ; The CONTRAST statement provides a mechanism for obtaining custom hypothesis tests. It is patterned after the CONTRAST statement in PROC GLM, although it has been extended to include random effects. This enables you to select an appropriate inference space (McLean, Sanders, and Stroup 1991).You can test the hypothesis , where L' = (K' M') and , in several inference spaces. The inference space corresponds to the choice of M. When M = 0, your inferences apply to the entire population from which the random effects are sampled; this is known as the broad inference space. When all elements of M are nonzero, your inferences apply only to the observed levels of the random effects. This is known as the narrow inference space, and you can also choose it by specifying all of the random effects as fixed. The GLM procedure uses the narrow inference space. Finally, by zeroing portions of M corresponding to selected main effects and interactions, you can choose intermediate inference spaces. The broad inference space is usually the most appropriate, and it is used when you do not specify any random effects in the CONTRAST statement. In the CONTRAST statement, label。
SAS学习系列32. 协方差分析资料报告
32. 协方差分析（一）原理一、基本思想在实际问题中，有些随机因素是很难人为控制的，但它们又会对结果产生显著影响。
如果忽略这些因素的影响，则有可能得到不正确的结论。
这种影响的变量称为协变量（一般是连续变量）。
例如，研究3种不同的教学方法的教学效果的好坏。
检查教学效果是通过学生的考试成绩来反映的，而学生现在考试成绩是受到他们自身知识基础的影响，在考察的时候必须排除这种影响。
协方差分析回归分析与方差分析的结合，在做两组和多组均值之间的比较前，用直线回归的方法找出各组因变量Y与协变量X之间的数量关系，求得在假定X相等时的修正均均值，然后用方差分析比较修正均值之间的差别。
简单来说，协方差分析就是扣除协变量的影响，或者将这些协变量处理成相等，再对修正的Y的均值作方差分析。
根据协变量的个数的不同，协方差分析分为一元协方差分析和多元协方差分析。
二、协方差分析需要满足的条件（1）自变量是分类变量，协变量是定距变量，因变量是连续变量；对连续变量或定距变量的协变量的测量不能有误差；（2）协变量与因变量之间的关系是线性关系，可以用协变量和因变量的散点图来检验是否违背这一假设；协变量的回归系数（即各回归线的斜率）是相同的，且不等于0，即各组的回归线是非水平的平行线。
否则，就有可能犯第一类错误，即错误地接受虚无假设；（3）自变量与协变量相互独立，若协方差受自变量的影响，那么协方差分析在检验自变量的效应之前对因变量所作的控制调整将是偏倚的，自变量对因变量的间接效应就会被排除；（4）各样本来自具有相同方差σ2的正态分布总体，即要求各组方差齐性。
三、基本理论1. 观测值=均值+分组变量影响+协变量影响+随机误差. 即()ij i ij ij y u t x x βε=++-+ （1）其中，X 为所有协变量的平均值。
注：在方差分析中，协变量影响是包含在随机误差中的，在协方差分析中需要分离出来。
用协变量进行修正，得到修正后的y ij (adj)为(adj)()ij ij ij i ij y y x x u t βε=--=++就可以对y ij (adj)做方差分析了。
SAS过程步及其语句§1过程步及其语句
SAS过程步及其语句§1过程步及其语句在SAS中，过程步是一种用于执行特定任务的程序步骤。
每个过程步都由一个或多个语句组成，这些语句用于指示SAS如何执行特定的操作。
以下是一些常用的SAS过程步及其相关的语句：
1.DATA步：用于读取和处理数据集。
-DATA语句：指定要创建或修改的数据集的名称。
-SET语句：指定要读取的数据集。
-BY语句：按照一些变量进行排序。
2.PROC步：用于执行各种统计分析和数据处理任务。
-PROC语句：指定要执行的过程。
-DATA语句：指定要分析的数据集。
-VAR语句：指定要分析的变量。
3.SORT步：用于对数据集按照指定变量进行排序。
-SORT语句：指定要排序的数据集和排序变量。
-BY语句：按照一些变量进行排序。
4.PRINT步：用于输出数据或结果。
-PRINT语句：指定要输出的数据集和变量。
5.MERGE步：用于合并两个或多个数据集。
-MERGE语句：指定要合并的数据集和合并变量。
6.TRANSPOSE步：用于转置数据集。
-TRANSPOSE语句：指定要转置的数据集和转置变量。
这些是SAS中常用的一些过程步及其语句，根据具体的数据处理或统计分析任务，还可以使用其他过程步及其相关的语句。
20个SAS过程步
20个SAS过程步
1、PROC MEANS--数据描述：计算均数、标准差、最大值、最小值、变量有效数据个数、变量缺失个数
2、PROC UNIVARIATE--正态性检验
3、PROC TTEST--两独立样本检验
4、PROC NPAR1WAR--秩和检验
5、PROC ANOVA--方差分析
6、PROC CORR--相关性分析
7、PROC REG--回归分析
8、PROC FREQ--计数资料描述；卡方检验；诊断试验
9、PROC LOGISTIC--结局是二分类的Logisitc回归分析
10、PROC PHREG--生存分析
11、PROC POWER--样本量及把握度计算
12、PROC PRINT--显示数据集
13、PROC GLM--回归分析或协方差分析
14、PROC RANK--给某变量排次或按序分组
15、PROC SORT--按某变量排序
16、PROC SURVEYSELECT--概率抽样
17、PORC IMPORT--导入数据集
18、PROC EXPORT--导出数据集
19、PROC CONTENTS--产生一个数据集的头文件，包含了多种该数据集的信息
20、PROC TABULATE--输出报表。
几种描述性统计分分析的SAS过程
1. PROC MEANS过程
计算SAS数据集中各变量值的位置、分散性、分布形状等数字特征。
基本语句：
PROC MEANS options; VAR variables; OUTPUT OUT=dataset name keyword=name … ; RUN;
说明: (a) “options”一般选项为： (i)以DATA=SAS dataset name指定所分析的SAS数据集名称； (ii) 指定欲计算的特征数字名称（关键词，由SAS系统规定）， 包括 N, MEAN, STD, VAR, MIN, MAX, RANGE, SUM, USS, CSS, SKEWNESS, KURTOSIS等。
(b) 该过程第二句和第三句的用法与PROC MEANS过程基本相同，只 是在“keyword=name”中的“name”不可省略，必须由用户给相
应关 键词赋予具体名称。
(c) PROC UNIVARIATE过程的默认输出结果除包括PROC MEANS 中全部关键词所对应的特征数字以及中位数等外，还有如下关键 词选项： Q1: 下四分位数； Q3: 上四分位数； QRANG: 四分位极差； P1: 1%分位数； P5: 5%分位数； P10: 10%分位数； P90: 90%分位数； P95: 95%分位数； P99: 99%分位数。
(2)作经验分布函数曲线及拟合的分布函数曲线 基本语句为： PROC CAPABILITY options; CDFPLOT variables/options; RUN;
(3)作QQ图 基本语句为： PROC CAPABILITY options; QQPLOT variables/options; RUN;
SAS：SAS常用过程之统计描述过程procunivariate
SAS：SAS常用过程之统计描述过程procunivariatefrom：/s/blog_5f049388010170ab.html FROM :/qiaozhanwen@126/blog/static/ 12955392520128225952558/-proc univariate统计量：----------------------------------------------------------------------------------------------------------------------------------默认：[plain] view plain copy1.1.观测值（未缺失的）2.2.平均值3.3.方差4.4.标准差5.5.偏系数6.6.峭度系数7.7.未校正和校正后的平方和8.8.差异系数（相对标准差）9.9.平均数的标准误10.10.比较变量值是否等于0 的t检验11.11.最大值12.12.最小值13.13.全距范围14.14.中数，第3和第2四分位数15.15.四分位差16.16.众数17.17.第1、2、10、90、95和99的百分位数18.18.5个最大值和5个最小值需指定的（加上选项normal和plot）：[plain] view plain copy1.19.W或D统计量，检验数据是否正太分布2.20.茎叶图3.21.箱式图4.22.正太概率图，将累加频数分布和理想正太分布相比较-proc univariate统计结果的一些说明：----------------------------------------------------------------------------------------------------------------------------------1、极值观测：极端观测列出了数据中最大和最小的5个值，每个极端数据旁边还有数据的编号。
sas中proc mixed迭代历史解读
在SAS中，PROC MIXED是一种用于进行混合效应模型分析的程序。
混合效应模型是一种线性模型，它包括固定效应和随机效应两部分。
PROC MIXED可以用于拟合各种类型的混合效应模型，并提供了广泛的选项和方法来处理各种类型的数据结构和问题。
当使用PROC MIXED进行迭代时，SAS会尝试找到能够最小化残差平方和的参数估计值。
迭代过程通常包括以下步骤：
1. 初始化：SAS会为固定效应和随机效应的参数分配初始值。
这些初始值可以是随机生成的，也可以是用户提供的。
2. 固定效应优化：SAS会使用初始参数估计值来拟合固定效应部分，并计算出固定效应的估计值。
3. 随机效应优化：接下来，SAS会使用固定效应的估计值来拟合随机效应部分，并计算出随机效应的估计值。
4. 迭代更新：SAS会将固定效应和随机效应的估计值更新为最新的最优值，并重复步骤2和3，直到达到收敛条件。
5. 收敛判断：在每次迭代后，SAS会检查固定效应和随机效应的估计值是否已经收敛。
如果估计值的变化小于预设的阈值或达到预设的最大迭代次数，则认为模型已经收敛。
6. 结果输出：一旦模型收敛，SAS会输出固定效应和随机效应的估计值，以及相关的统计量和图形。
通过解读PROC MIXED的迭代历史，可以了解模型的拟合情况、参数估计值的稳定性以及模型的优劣等方面。
通常，迭代历史会包括每次迭代的固定效应和随机效应的估计值、残差平方和的变化等信息。
通过分析这些信息，可以判断模型是否合适，并对模型进行改进或调整。
SAS过程步操作基础
proc means语句的主要选项
missing：将class变量的缺失值作为合法的水平用以 创建代表分组的组合； fw=：指定输出结果中显示有关统计量的列的宽度； maxdec=：指定一个0~8的整数，用以设置输出结果 中有关统计量的最大小数位数； noprint：禁止在结果窗口显示任何分析结果； alpha=：指定均数可信区间的置信水平，默认值为 0.05。
字符排列顺序
字符型变量： blank ! “ # $ % & „ ( ) * + , - / 0 1 2 3 4 5 6 7 8 9:;<=>?@ABCDEFGHIJKLMN OPQRSTUVWXYZ[\]^_`abcdef ghIghIjklmnopqrstuvwxyz{|}~ 数值型变量： 缺失值 (._ . .A to .Z) 数值 ( 依照大小顺序 )
print过程示例
data test;
do i=1 to 20;
do j=1 to 5; x=i*j/2; y=i**2*j; t=sqrt(i*j); output; end; end; label x=„one' y=„tow' t='three'; run;
proc sort data=test; by j; run;
proc contents语句的主要选项
ห้องสมุดไป่ตู้
detials|nodetials ：用于控制显示结果的详尽程度。 前者将显示上述的全部内容，后者则仅显示有关变量 信息的部分。默认设置：detials。 varnum ：要求将变量按照其在数据集中的排列顺序 而非字母顺序显示。 short ：有关变量信息部分仅显示变量名称，不显示 变量属性。 out= ：将输入数据集中有关变量的信息存储到指定的 数据集中。 noprint ：禁止程序运行结果在output窗口的输出显示。
SAS学习系列29. 方差分析Ⅱ—ANOVA,GLM过程步
28. 方差分析Ⅱ—ANOVA,GLM过程步SAS提供了ANOV A和GLM过程步进行方差分析。
ANOV A过程步主要处理均衡数据（分类变量的每个水平的观察数是相等），该过程考虑到均衡设计的特殊构造，处理起来速度更快更省内存，也可以处理拉丁方设计、若干不完全的均衡区组设计数据等。
若试验设计不均衡，也不是前面几种实验设计数据，则应该使用GLM过程。
（一）PROC ANOV A过程步一、基本语法PROC ANOV A data=数据集<可选项> ;CLASS 分类变量列表;MODEL 因变量=效应变量列表</可选项>;<MEANS 效应变量列表</可选项> ;><TEST <H=效应变量列表> E=效应变量列表;>说明：（1）CLASS语句是必不可少的，必须放在MODEL语句之前，用来指定分类、区组变量（单因素方差分析只有一个变量）；（2）MODEL语句也是必不可少的，该语句用来规定因变量和自变量效应（单因素方差分析的自变量就是分类变量）。
若没有规定自变量的效应，则只拟合截距，假设检验为因变量的均值是否为0. Model语句的主要形式有4种：①主效应模型model y=a b c;②含有交叉因素的模型model y=a b c a*b a*c b*c a*b*c;③嵌套模型model y=a b c(a b);④包含嵌套、交叉和主效应的模型model y=a b(a) c(a) b*c(a);（3）MEANS语句必须出现在MODEL语句之后，用来计算在效应变量所对应的因变量均值，但这些均值没有针对模型中的效应进行修正。
若要计算修正的均值需要用GLM过程步的LSMEANS语句；（4）MEANS语句的可选项主要有两个内容，一是选择多重比较的检验方法，二是设定这些检验的参数（只能用于主效应）；bon——对所有主效应均值之差进行Bonferroni的t检验；duncan——对所有主效应均值进行Duncan的多重极差检验；smm|gt2——当样本量不等时，基于学生化最大模和Sidak不相关t不等式，等到Hochberg的GT2方法，对主效应均值进行两两对比检验；snk——对所有主效应均值进行Student-Newman-Keuls的多重极差检验；t|lsd——对所有主效应均值进行两两t检验，它相当于在单元观察数相等时Fisher的最小显著差检验；tukey——对所有主效应均值进行Tukey的学生化极差检验；waller——对所有主效应均值进行Waller-Duncan的k比率检验；……alpha=p——设置显著水平；clm——对变量的每个水平的均值按置信区间形式输出；e=效应变量——指定在多重对比检验中所使用的误差均方。
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Introduction to PROC MIXEDTable of Contents1.Short description of methods of estimation used in PROC MIXED2.Description of the syntax of PROC MIXED3.References4. Examples and comparisons of results from MIXED and GLM- balanced data: fixed effect model and mixed effect model,- unbalanced data, mixed effect model1. Short description of methods of estimation used in PROC MIXED.The SAS procedures GLM and MIXED can be used to fit linear models. Proc GLM was designed to fit fixed effect models and later amended to fit some random effect models by including RANDOM statement with TEST option. The REPEATED statement in PROC GLM allows to estimate and test repeated measures models with an arbitrary correlation structure for repeated observations. The PROC MIXED was specifically designed to fit mixed effect models. It can model random and mixed effect data, repeated measures, spacial data, data with heterogeneous variances and autocorrelated observations.The MIXED procedure is more general than GLM in the sense that it gives a user more flexibility in specifying the correlation structures, particularly useful in repeated measures and random effect models. It has to be emphasized, however, that the PROC MIXED is not an extended, more general version of GLM. They are based on different statistical principles; GLM and MIXED use different estimation methods. GLM uses the ordinary least squares (OLS) estimation, that is, parameter estimates are such values of the parameters of the model that minimize the squared difference between observed and predicted values of the dependent variable. That approach leads to the familiar analysis of variance table in which the variability in the dependent variable (the total sum of squares) is divided into variabilities due to different sources (sum of squares for effects in the model). PROC MIXED does not produce an analysis of variance table, because it uses estimation methods based on different principles. PROC MIXED has three options for the method of estimation. They are: ML (Maximum Likelihood), REML (Restricted or Residual maximum likelihood, which is the default method) and MIVQUE0 (Minimum Variance Quadratic Unbiased Estimation). ML and REML are based on a maximum likelihood estimation approach. They require the assumption that the distribution of the dependent variable (error term and the random effects) is normal. ML is just the regular maximum likelihood method,that is, the parameter estimates that it produces are such values of the model parameters that maximize the likelihood function. REML method is a variant of maximum likelihood estimation; REML estimators are obtained not from maximizing the whole likelihood function, but only that part that is invariant to the fixed effects part of the linear model. In other words, if y = X b + Zu + e, where X b is thefixed effects part, Zu is the random effects part and e is the error term, then the REML estimates are obtained by maximizing the likelihood function of K'y, where K is a full rank matrix with columns orthogonal to the columns of the X matrix, that is, K'X= 0. It leads to REML estimator of the variance-covariance matrix of y, say V. It does not depend on the choice of matrix K. Then the generalized least squares equations, known also from the weighted least squares approach and the GLM procedure,X'(inverse of V)X b=X'(inverse of V)y,where V is replaced with its estimator, are solved to obtain the estimates of fixed effects parameters b.It is assumed that the random effects u and the error vector e are normally distributed, uncorrelated and have expectations 0. Under the assumption that u and e are not correlated, V, the variance-covariance matrix of y, is equal to ZGZ’ + R, where G and R are the variance matrices of u and e, respectively.Estimators of V, the variance-covariance matrix of y, can also be obtained in PROC MIXED by the MIVQUE0 method. For a short description of the method see reference (3), p.506. This method has two advantages over ML and REML; it does not require normality assumption (for computing the estimators) as do ML and REML and does not involve iterations. However simulation studies by Swallow and Monahan (1984) present evidence favoring ML and REML over MIVQUE0. PROC MIXED uses MIVQUE0 as starting values for the ML and RELM procedures.For balanced data the REML method of PROC MIXED provides estimators and hypotheses test results that are identical to ANOVA (OLS method of GLM), provided that the ANOVA estimators of variance components are not negative. The estimators, as in GLM, are unbiased and have minimum variance properties. The ML estimators are biased in that case. In general case of unbalanced data neither the ML nor the REML estimators are unbiased and they do not have to be equal to those obtained from PROC GLM. There are many models involving forms of variance-covariance structure of observations that can not be analyzed using PROC GLM with TEST or PROC GLM with the REPEATED options. PROC MIXED can handle such cases. It also has to be mentioned that PROC GLM was design for analysis of fixed effects models and all computations are done under the assumption that there is only one variance component in the model, the error term. The RANDOM statement with the TEST option can be used to get the right tests in the case random effects are present in the model, but still some printed results, variances and standard errors, will be incorrect.2. Description of the syntax of PROC MIXEDThe PROC MIXED syntax is similar to the syntax of PROC GLM. There are, however, a few important differences. The random effects and repeated statements are used differently, random effects are not listed in the model statement, GLM has MEANS and LSMEANS statements, whereas MIXED has only the LSMEANS statement, GLM offers Type I, II, III and IV tests for fixed effects, while MIXED offers TYPE I and TYPE III. The following is a general form of PROC MIXED statement: PROC MIXED options;CLASS variable-list;MODEL dependent=fixed effects/ options;RANDOM random effects / options;REPEATED repeated effects / options;CONTRAST 'label' fixed-effect values | random-effect values/ options;ESTIMATE 'label' fixed-effect values | random-effect values/ options;LSMEANS fixed-effects / options;MAKE 'table' OUT= SAS-data-set < options >;RUN;The CONTRAST, ESTIMATE, LSMEANS, MAKE and RANDOM statements can appear multiple times, all other statements can appear only once.The PROC MIXED and MODEL statements are required. The MODEL statement must appear after the CLASS statement if CLASS statement is used. The CONTRAST, ESTIMATE, LSMEANS, RANDOM and REPEATED statement must follow the MODEL statement. CONTRAST and ESTIMATE statements must follow RANDOM statement if the RANDOM is used.A detailed description of all functions and options of each PROC MIXED statement is given inSAS/STAT Software Changes and Enhancements through Release 6.11 and SAS/STAT Software Changes and Enhancements for Release 6.12, SAS Institute Inc. (1996). The following is a short summary of selected, most often used, MIXED procedure statements.PROC MIXED <options>;Selected options:DATA= SAS data setNames SAS data set to be used by PROC MIXED. The default is the most recently created data set. METHOD=REMLMETHOD=MLMETHOD=MIVQUE0Specifies the estimation method. See Section 1 for a brief description of the methods and references. REML is the default method.COVTESTPrints asymptotic standard errors and Wald Z-test for variance-covariance structure parameter estimates. For example, if a random effect A is included in the model, then the estimator of the variance of A will be printed together with the Wald test of the hypothesis that the variance of A is 0.The COVTEST option is specified after Proc mixed and before semicolon;. For example,Proc mixed data=mydata method=reml covtest;CLASS variables;Lists classification variables (categorical independent variables in the model). For example:proc mixed data=mydata covtest;Class group gender agecat;MODEL dependent = fixed effects </options>;The model statement names a single dependent variable and the fixed effects, that is independent variables that are not random. An intercept is included in the model by default. The NOINT option can be used to remove the intercept.NOTE: Even though PROC MIXED allows only for one dependent variable in the model statement, it is possible to use it to model, for example, multivariate repeated measures. In such case, the data set has to be properly prepared and should contain a variable indicating the measurement type. The correlation between observations on the same unit has to be modeled properly with the REPEATED statement. For example, suppose your observed data consist of heights and weights of children measured over several successive years. Your input data set should then contain variables similar to the following:Y, all of the heights and weights, with a separate observation (line in the data file) for eachVAR, indicating whether the measurement is a height or a weightYEAR, indicating the year of measurementCHILD, indicating the child on which the measurement was taken.Selected Options of the model statement:CHISQ, request χ2 – tests (Wald tests) be performed for all fixed effects in addition to the F-tests. DDFM=RESIDUALDDFM=CONTAINDDFM=BETWITHNDDFM=SATTERTH,The DDFM= options specifies the method for computing the denominator degrees of freedom for the tests of fixed effects. DDFM=SATTERTH will result in the Satterthwaite approximation for the denominator degrees of freedom. For balanced designs with random effects it will produce the same test results as RANDOM …/ TEST option in PROC GLM (if the default METHOD=REML is used in proc mixed).P, requests that the predicted values be printed.RANDOM random effects </options>;The RANDOM statement defines the random effects in the model. It can be used to specify traditional variance components (independent random effects with different variances) or to list correlated random effects and specify a correlation structure for them with the TYPE=covariance-structure option. A variety of structures are available (see references 5 and 6), most often used are either TYPE=VC, a variance components correlation structure or TYPE=UN, an unstructured, that is, arbitrary covariance matrix. TYPE=VC is the default structure. In the following example, the effect of subject is random.Proc mixed data=one method=reml covtest;Class gender treat subject;Model y=gender treat gender*treat /ddfm=satterth;Random subject(gender);Run;In the next example there are two random effects specified (besides the error term) and it is assumed that they are correlated.Intercept and the slope coefficient in the regression equation have fixed and random parts which are assumed to be correlated. The model is:yij = a0 +aj + b0*time + bj*time + eij, where yij is observation i for person j.The random effects, aj, bj and eij, are asumed to have normal distributions with mean zero and different variances and it is also assumed that aj and bj are correlated.Proc mixed data=one method=reml covtest;Class person;Model y=time /solution;Random intercept time /type=un subject=person;Run;REPEATED repeated effects / options;The repeated statement is used in PROC MIXED to specify the covariance structure of the error term. The repeated effect has to be categorical and has to appear in the class statement and the data has to be sorted accordingly. For example, suppose that for each subject a measurement was taken at five equally spaced time points. The time is the repeated effect and the data has to be sorted by subject and time within each subject. If time is also used as a continuous independent variable in the model then a new variable, say t, identical to time has to be defined and t should be used in the class and repeated statements. For example:Data one;Set one;T=time;Run;Proc sort data=one;By group id t;Run;Proc mixed data=one covtest;Class t group id;Model y=group time group*time;Repeated t /type=ar(1) subject=id;Run;The option TYPE in the REPEATED statement specifies the type of the error correlation structure. The one specified in the above example is the first-order autoregressive correlation. The subject option is needed to identify observations that are correlated. Observations within the same subject are correlated with the type of correlation specified in TYPE, observations from different subjects are independent.The TYPE option allows for many types of correlation structures. Most commonly used are autocorrelation, compound symmetry, Huynh-Feldt, Toeplitz, variance components, unstructured and spatial. For the complete list and examples, see references (7) and (8).CONTRAST ‘label’ fixed-effect values | random-effect values / options;ESTIMATE ‘label’ fixed-effect values | random-effect values / options;The CONTRAST statement is used when there is need for custom hypothesis tests, the ESTIMATE statement, when there is need for custom estimates. Although they were extended in PROC MIXED to include random effects, their use is very similar to the CONTRAST and ESTIMATE statement in PROC GLM.LABEL is required for every contrast or estimate statement. It identifies the contrast or estimated parameter on the output. It can not be longer than 20 characters.FIXED-EFFECT is the name of an effect appearing in the MODEL statement.RANDOM-EFFECT is the name of an effect appearing in the RANDOM statement.VALUES are the coefficients of the contrast to be tested or the parameter to be estimated.For example, suppose that we want to test if there is a significant effect of treat in group 2, where treat has three levels and group four levels. We also want to estimate the mean for treat 1 in group 2, the mean for treat 2 in group 2 and the difference between these two means. We will need the following CONTRAST and ESTIMATE statements to obtain these results.Proc mixed data=one method=reml covtest;Class group treat subject;Model y=group treat group*treat /ddfm=satterth;Random subject(group);Contrast ‘treat in group 2’Treat 1 –1 0 group*treat 0 0 0 1 –1 0 0 0 0 0 0 0,Treat 0 1 –1 group*treat 0 0 0 0 1 –1 0 0 0 0 0 0;Estimate ‘treat1 group2 mean’ intercept 1 group 0 1 0 0 treat 1 0 0group*treat 0 0 0 1 0 0 0 0 0 0 0 0;Estimate ‘treat2 group2 mean’ intercept 1 group 0 1 0 0 treat 0 1 0Group*treat 0 0 0 0 1 0 0 0 0 0 0 0;Estimate ‘mean diff t1g2-t2g2’ Treat 1 –1 0 group*treat 0 0 0 1 –1 0 0 0 0 0 0 0;Run;LSMEANS fixed-effects / options;LSMEANS computes the least squares means of fixed effects. The ADJUST option requests a multiplecomparison adjustment to the p-values for pair-wise comparisons of means. The following adjustments are available: BON (Bonferroni), DUNNET, SCHEFFE, SIDAK, SIMULATE, SMM|GT2 and TUKEY. The ADJUST option results in all possible pair-wise comparisons. If comparisons with a control level are only needed then in addition to ADJUST option, PDIFF=control should be used. The SLICE option allows to test the significance of one effect at each level of another effect.For example, suppose that we want to compute the least squares means for group*treat and do pair-wise comparisons with the control being group 1 and treat 1. We also want to test for the significance of the treat effect within each group level using the SLICE option..Proc mixed data=one method=reml covtest;Class group treat subject;Model y=group treat group*treat /ddfm=satterth;Random subject(group);lsmeans group*treat /adjust=bon pdiff=control('1' '1') slice=group;Run;MAKE 'table' OUT= SAS-data-set < options >;The MAKE statement converts any table produced by PROC MIXED into a sas data set. NOPRINT option can be used to prevent printing the requested table. Only requested or default output can be converted into a sas data set. Hence, in particular, the P option has to be used in the model statement to produce a data set with predicted values, and the LSMEANS statement has to be included to output least squares means. For example,Proc mixed data=one method=reml covtest;Class group treat subject;Model y=group treat group*treat /ddfm=satterth p;Random subject(group);lsmeans group*treat /adjust=bon pdiff=control('1' '1') slice=group;make ‘LSMeans’ out=gtmeans;make ‘predicted’ out=pred noprint;Run;Proc print data=gtmeans;Proc print data=pred;Run;ReferencesStatistics Books:1. Searle, Shayle R. (1987). Linear Models For Unbalanced Data, John Wiley & Sons.2. Searle, Shayle R. (1971). Linear Models, John Wiley & Sons.3. Searle, S.R., Casella, G., and McCulloch, C.E. (1992), Variance Components. John Wiley&Sons.4. Verbeke, G., Molenberghs, G. (Editors) (1997), Linear Mixed Models in Practice. A SAS-Oriented Approach. Springer-VerlagSAS Institute Books:5. Littell, Ramon C., Milliken, George A., Stroup, Walter W., Wolfinger, Russell D. (1996). SAS System For Mixed Models, SAS Institute Inc.6. SAS Institute Course Notes (1996). Advanced General Linear Models with an Emphasis on Mixed Models, SAS Institute Inc.7. SAS/STAT Software Changes and Enhancements through Release 6.11, SAS Institute Inc. 1996.8. SAS/STAT Software Changes and Enhancements for Release 6.12, SAS Institute Inc. 1996.3. Examples and comparisons of the results from PROC MIXED and PROC GLM. Example1. Fixed effect model, balanced data.In this example, 36 subjects are randomly assigned to 12 group – treatment combinations, 3 to each combination. There are three treatments and four groups. In the following program, factor treat with 3 levels is the effect of the treatment and factor group with 4 levels is the effect of the group.As you can see below, the results from both procedures are identical.Program:options ls=76;data one;input y group treat subject;cards;22 1 1 123 1 1 225 1 1 317 1 2 418 1 2 523 1 2 612 1 3 716 1 3 814 1 3 98 2 1 109 2 1 1110 2 1 1216 2 2 1317 2 2 1420 2 2 1529 2 3 1630 2 3 1736 2 3 183 3 1 197 3 1 205 3 1 211 32 222 3 2 231 32 244 3 3 257 3 3 268 3 3 2711 4 1 2815 4 1 298 4 1 3034 4 2 3137 4 2 3233 4 2 3327 4 3 3428 4 3 3524 4 3 36;run;Proc mixed data=one method=reml;Class group treat;Model y=group treat group*treat;lsmeans group*treat /adjust=bon pdiff=control('1' '1') slice=group;Contrast 'treat in group 2'Treat 1 -1 0 group*treat 0 0 0 1 -1 0 0 0 0 0 0 0,Treat 0 1 -1 group*treat 0 0 0 0 1 -1 0 0 0 0 0 0;Estimate 'treat1 group2 mean' intercept 1 group 0 1 0 0 treat 1 0 0group*treat 0 0 0 1 0 0 0 0 0 0 0 0;Estimate 'treat2 group2 mean' intercept 1 group 0 1 0 0 treat 0 1 0Group*treat 0 0 0 0 1 0 0 0 0 0 0 0;Estimate 'mean diff t1g2-t2g2' Treat 1 -1 0 group*treat 0 0 0 1 -1 0 0 0 0 0 0 0; Run;proc GLM data=one;class group treat;Model y=group treat group*treat;lsmeans group*treat /adjust=bon pdiff=control('1' '1') slice=group;Contrast 'treat in group 2'Treat 1 -1 0 group*treat 0 0 0 1 -1 0 0 0 0 0 0 0,Treat 0 1 -1 group*treat 0 0 0 0 1 -1 0 0 0 0 0 0;Estimate 'treat1 group2 mean' intercept 1 group 0 1 0 0 treat 1 0 0group*treat 0 0 0 1 0 0 0 0 0 0 0 0;Estimate 'treat2 group2 mean' intercept 1 group 0 1 0 0 treat 0 1 0Group*treat 0 0 0 0 1 0 0 0 0 0 0 0;Estimate 'mean diff t1g2-t2g2' Treat 1 -1 0 group*treat 0 0 0 1 -1 0 0 0 0 0 0 0; Run;Results:The MIXED ProcedureGROUP 4 1 2 3 4TREAT 3 1 2 3Tests of Fixed EffectsSource NDF DDF Type III F Pr > FGROUP 3 24 121.60 0.0001TREAT 2 24 34.11 0.0001GROUP*TREAT 6 24 43.04 0.0001ESTIMATE Statement ResultsParameter Estimate Std Error DF t Pr > |t|treat1 group2 mean 9.00000000 1.35400640 24 6.65 0.0001treat2 group2 mean 17.66666667 1.35400640 24 13.05 0.0001mean diff t1g2-t2g2 -8.66666667 1.91485422 24 -4.53 0.0001CONTRAST Statement ResultsSource NDF DDF F Pr > Ftreat in group 2 2 24 71.35 0.0001Least Squares MeansEffect GROUP TREAT LSMEAN Std ErrorGROUP*TREAT 1 1 23.33333333 1.35400640GROUP*TREAT 1 2 19.33333333 1.35400640GROUP*TREAT 1 3 14.00000000 1.35400640GROUP*TREAT 2 1 9.00000000 1.35400640GROUP*TREAT 2 2 17.66666667 1.35400640GROUP*TREAT 2 3 31.66666667 1.35400640GROUP*TREAT 3 1 5.00000000 1.35400640GROUP*TREAT 3 2 1.33333333 1.35400640GROUP*TREAT 3 3 6.33333333 1.35400640GROUP*TREAT 4 1 11.33333333 1.35400640GROUP*TREAT 4 2 34.66666667 1.35400640GROUP*TREAT 4 3 26.33333333 1.35400640Differences of Least Squares MeansEffect GROUP TREAT GROUP _TREAT Difference Std Error DF GROUP*TREAT 1 2 1 1 -4.00000000 1.91485422 24 GROUP*TREAT 1 3 1 1 -9.33333333 1.91485422 24 GROUP*TREAT 2 1 1 1 -14.33333333 1.91485422 24 GROUP*TREAT 2 2 1 1 -5.66666667 1.91485422 24 GROUP*TREAT 2 3 1 1 8.33333333 1.91485422 24 GROUP*TREAT 3 1 1 1 -18.33333333 1.91485422 24 GROUP*TREAT 3 2 1 1 -22.00000000 1.91485422 24 GROUP*TREAT 3 3 1 1 -17.00000000 1.91485422 24 GROUP*TREAT 4 1 1 1 -12.00000000 1.91485422 24 GROUP*TREAT 4 2 1 1 11.33333333 1.91485422 24 GROUP*TREAT 4 3 1 1 3.00000000 1.91485422 24Differences of Least Squares Meanst Pr > |t| Adjustment Adj P-2.09 0.0475 Bonferroni 0.5224-4.87 0.0001 Bonferroni 0.0006-7.49 0.0001 Bonferroni 0.0000-2.96 0.0068 Bonferroni 0.07524.35 0.0002 Bonferroni 0.0024-9.57 0.0001 Bonferroni 0.0000-11.49 0.0001 Bonferroni 0.0000-8.88 0.0001 Bonferroni 0.0000-6.27 0.0001 Bonferroni 0.00005.92 0.0001 Bonferroni 0.00001.57 0.1303 Bonferroni 1.0000Tests of Effect SlicesEffect GROUP NDF DDF F Pr > FGROUP*TREAT 1 2 24 11.96 0.0002GROUP*TREAT 2 2 24 71.35 0.0001GROUP*TREAT 3 2 24 3.66 0.0411GROUP*TREAT 4 2 24 76.26 0.0001General Linear Models ProcedureClass Level InformationGROUP 4 1 2 3 4TREAT 3 1 2 3General Linear Models ProcedureDependent Variable: YSum of MeanSource DF Squares Square F Value Pr > F Model 11 3802.00000 345.63636 62.84 0.0001 Error 24 132.00000 5.50000Corrected Total 35 3934.00000R-Square C.V. Root MSE Y Mean0.966446 14.07125 2.34521 16.6667Source DF Type III SS Mean Square F Value Pr > F GROUP 3 2006.44444 668.81481 121.60 0.0001 TREAT 2 375.16667 187.58333 34.11 0.0001 GROUP*TREAT 6 1420.38889 236.73148 43.04 0.0001General Linear Models ProcedureLeast Squares MeansAdjustment for multiple comparisons: BonferroniGROUP TREAT Y Pr > |T| H0:LSMEAN LSMEAN=CONTROL1 1 23.33333331 2 19.3333333 0.52241 3 14.0000000 0.00062 1 9.0000000 0.00012 2 17.6666667 0.07522 3 31.6666667 0.00243 1 5.0000000 0.00013 2 1.3333333 0.00013 3 6.3333333 0.00014 1 11.3333333 0.00014 2 34.6666667 0.00014 3 26.3333333 1.0000GROUP*TREAT Effect Sliced by GROUP for YSum of MeanGROUP DF Squares Square F Value Pr > F1 2 131.555556 65.777778 11.9596 0.00022 2 784.888889 392.444444 71.3535 0.00013 2 40.222222 20.111111 3.6566 0.04114 2 838.888889 419.444444 76.2626 0.0001Dependent Variable: YContrast DF Contrast SS Mean Square F Value Pr > Ftreat in group 2 2 784.888889 392.444444 71.35 0.0001T for H0: Pr > |T| Std Error ofParameter Estimate Parameter=0 Estimatetreat1 group2 mean 9.0000000 6.65 0.0001 1.35400640treat2 group2 mean 17.6666667 13.05 0.0001 1.35400640mean diff t1g2-t2g2 -8.6666667 -4.53 0.0001 1.91485422Example 2. Mixed effect model, balanced data.In this example, 12 subjects are randomly assigned to 4 groups, 3 to each group. There are three observations for each subject corresponding to measurements taken at time 1, 2 and 3. In the following program, factor time with 3 levels is the effect of the time and factor group with 4 levels is the effect of the group.A mixed effect model with fixed effect of group and time and random effect of subject will be used to analyze the data. It is assumed that the effect of the subject has a normal distribution with mean 0 and variance sigmaS squared (it measures between subject variability). It is also assumed that the error term has a normal distribution with mean 0 and variance sigmaE squared (it measures within subject error) and the error and subject effects are not correlatedAs you can see below, the results of MIXED and GLM are not identical. The F and p-values for the tests are the same. Values from proc mixed have to be compared with the Tests of Hypotheses for MixedModel Analysis from proc GLM, not with the main, General Linear Model Procedure, ANOVA table. The values in the main ANOVA table in proc GLM are incorrect for this example; they are computed under the assumption that subject is a fixed effect. However, the standard error of the lsmeans and requested estimates are not the same for proc MIXED and proc GLM. The ones printed by proc MIXED are correct. Again, proc GLM computed the standard error assuming that the subject effect is fixed. Note that the standard error for the third estimate, the mean difference between time 1 and time 2 in group 2 is the same for both. This is because when you compute that difference, the effect of the subject cancels out.Also note that proc GLM results printed in the Test of Hypotheses table include the F-test for the significance of the subject effect. The test is not printed in proc Mixed. The corresponding table includes only the fixed effects. The estimates of the random effects, in this case sigmaS squared (variance of the subject effect) and sigmaE squared (variance of the error term) are printed in the table named Covariance Parameter Estimates. The test of significance is the Wald test. The estimates are consistent with the proc GLM results. The residual variance in proc MIXED is the same as MSS (mean sum of squares) for the error in proc GLM. The subject variance can be computed from the GLM Type III Expected Mean Square table.Type III Expected Mean SquareGROUP Var(Error) + 3 Var(SUBJECT(GROUP)) + Q(GROUP,GROUP*TIME)SUBJECT(GROUP) Var(Error) + 3 Var(SUBJECT(GROUP))TIME Var(Error) + Q(TIME,GROUP*TIME)GROUP*TIME Var(Error) + Q(GROUP*TIME)According to that table, MSS(subject)=var(error)+3*var(subject). Hence var(subject)=(MSS(subject) – var(error))/3. Since the expected mean of MSS(error)=var(error), we can use MSS(error) as the estimate of var(error) and replace var(error) with MSS(error) in the above formula. Thus,Var(subject)=(12.5278 – 1.9861)/3=3.5139,which is the same as the value printed in the proc MIXED Covariance Parameter Estimates table for the subject.Program:options ls=76;data one;input y group time subject;cards;22 1 1 123 1 1 225 1 1 317 1 2 118 1 2 223 1 2 312 1 3 116 1 3 214 1 3 38 2 1 49 2 1 510 2 1 616 2 2 417 2 2 520 2 2 629 2 3 430 2 3 536 2 3 63 3 1 77 3 1 85 3 1 91 32 72 3 2 81 32 94 3 3 77 3 3 88 3 3 911 4 1 1015 4 1 118 4 1 1234 4 2 1037 4 2 1133 4 2 1227 4 3 1028 4 3 1124 4 3 12;run;proc sort data=one;by group subject time;run;Proc mixed data=one method=reml covtest;Class group time subject;Model y=group time group*time / DDFM=SATTERTH;RANDOM SUBJECT(group);lsmeans group*time /adjust=bon pdiff=control('1' '1') slice=group;Contrast 'time in group 2'time 1 -1 0 group*time 0 0 0 1 -1 0 0 0 0 0 0 0,time 0 1 -1 group*time 0 0 0 0 1 -1 0 0 0 0 0 0;Estimate 'time1 group2 mean' intercept 1 group 0 1 0 0 time 1 0 0group*time 0 0 0 1 0 0 0 0 0 0 0 0;Estimate 'time2 group2 mean' intercept 1 group 0 1 0 0 time 0 1 0Group*time 0 0 0 0 1 0 0 0 0 0 0 0;Estimate 'mean diff t1g2-t2g2' time 1 -1 0 group*time 0 0 0 1 -1 0 0 0 0 0 0 0; Run;proc GLM data=one;class group time subject;。