根据是否已知方差,分为两类检验:U检验和T检验。(当为μ即均值,σ是方差) 如果已知方差,则使用U检验,如果方差未知则采取T检验。【汪海波:当样本含量 n 较大时,样本均数符合正态分布,故可用 u 检验进行分析。当样本含量 n 小时,若观察值 x 符合正态分布,则用 t 检验(因此时样本均数符合 t 分布),当 x 为未知分布时,则应采用秩和检验。Wilcoxon的秩和检验(rank sum test)不依赖于总体分布的具体形式。】
1.2、有关参数方差σ2的假设检验
F检验是对两个正态分布的方差齐性检验,简单来说,就是检验两个分布的方差是否相等。【汪海波:t 检验和 u 检验不适用于多个样本均数的比较,因多次比较置信度下降。R.A.Fisher 的方差分析(analysis of variance,ANOVA)以 F 命名其统计量,又名 F 检验。】
library(nlme)#FitGaussianlinearandnonlinearmixed-effectsmodelslibrary(lme4)#Fitlinearandgeneralizedlinearmixed-effectsmodelslibrary(epiR)#Analysisofepidemiologicaldatalibrary(epicalc)#Functionsforepidemiologicalcalculationslibrary(lattice)#Datavisualizationsystemlibrary(epiDisplay)## IMPORT DATA
#-------------------------------
dropout.dat<-read.table("./data_dropout.csv",sep=",",na.string=" ",header=TRUE,dec=".")## Linear mixed model
#-------------------------------
cat("LINEAR MIXED MODEL WITH SYMMETRIC COVARIANCE MATRIXn")fit.m3<-lme(GFR~time+age+gender+micro+macro+micro:time+macro:time,random=list(patient=pdSymm(~1+time)),method="ML",data=dropout.dat,control=lmeControl(opt="optim"))#randomargument:isidenticaltorandom=~1+time|patientsummary(fit.m3)cat("95% CIn")coef.fit.m3<-summary(fit.m3)$tTableci(coef.fit.m3[,1],coef.fit.m3[,2],coef.fit.m3[,4])cat("VARIANCE-COVARIANCE MATRIXn")VarCorr(fit.m3)
输出结果:
> summary(fit.m3)
Linear mixed-effects model fit by maximum likelihood
Data: dropout.dat
AIC BIC logLik
9540.1 9602.84 -4758.05
Random effects:
Formula: ~1 + time | patient
Structure: General positive-definite
StdDev Corr
(Intercept) 10.426283 (Intr)
time 3.591427 -0.053
Residual 4.903330
Fixed effects: GFR ~ time + age + gender + micro + macro + micro:time + macro:time
Value Std.Error DF t-value p-value
(Intercept) 83.39609 3.242467 1175 25.719948 0.0000
time -1.74102 0.414817 1175 -4.197072 0.0000
age -0.28739 0.051564 195 -5.573483 0.0000
gender -2.61848 1.682065 195 -1.556703 0.1212
micro -18.39949 1.876851 195 -9.803381 0.0000
macro -26.56472 1.898283 195 -13.994078 0.0000
time:micro -2.92088 0.638801 1175 -4.572445 0.0000
time:macro -3.09101 0.670447 1175 -4.610374 0.0000
Correlation:
(Intr) time age gender micro macro time:micr
time -0.039
age -0.914 0.001
gender -0.018 0.000 -0.136
micro -0.169 0.067 -0.085 -0.002
macro -0.244 0.066 0.014 -0.108 0.425
time:micro 0.026 -0.649 -0.001 -0.002 -0.113 -0.043
time:macro 0.023 -0.619 0.001 -0.005 -0.041 -0.123 0.402
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-3.16590972 -0.60414300 -0.02061946 0.58097222 3.14244493
Number of Observations: 1378
Number of Groups: 200
> coef.fit.m3 <- summary(fit.m3)$tTable
> ci(coef.fit.m3[,1], coef.fit.m3[,2], coef.fit.m3[,4])
beta ci.low ci.up pvalue
(Intercept) 83.40 77.04 89.75 0.0000
time -1.74 -2.55 -0.93 0.0000
age -0.29 -0.39 -0.19 0.0000
gender -2.62 -5.92 0.68 0.1195
micro -18.40 -22.08 -14.72 0.0000
macro -26.56 -30.29 -22.84 0.0000
time:micro -2.92 -4.17 -1.67 0.0000
time:macro -3.09 -4.41 -1.78 0.0000
>
> cat("VARIANCE-COVARIANCE MATRIXn")
VARIANCE-COVARIANCE MATRIX
> VarCorr(fit.m3)
patient = pdSymm(1 + time)
Variance StdDev Corr
(Intercept) 108.70738 10.426283 (Intr)
time 12.89835 3.591427 -0.053
Residual 24.04265 4.903330