1.A very basic tutorial for performing linear mixed effects analyses（入门极品）
Tutorial 1: http://www.bodowinter.com/tutorial/bw_LME_tutorial1.pdf
Tutorial 2: http://www.bodowinter.com/tutorial/bw_LME_tutorial.pdf
<http://www.bodowinter.com/tutorial/bw_LME_tutorial.pdf>
nlme (Non-Linear Mixed Effects), lme4 (Linear Mixed Effects) and asreml
(average spatial real)
2.其它资料（Google搜索即有）
Mixed-Eects Models in R （较好）
An Appendix to An R Companion to Applied Regression, Second Edition
John Fox & Sanford Weisberg
Linear Mixed-Effects Models Using R（一本教材，进阶选用）
A Step-by-Step Approach
Andrzej Ga?ecki ? Tomasz Burzykowski
3.R中的线性混合模型介绍(简单了解不同的包）
http://blog.sciencenet.cn/blog-2577109-949820.html
https://www.r-bloggers.com/linear-mixed-models-in-r/
3.语法备忘
* 三种模型：
* AOD固定斜率，DAY随机截距：LMM.model = lmer(PM25 ~ AOD + (1|Day) , data=LMMexcdata)
* AOD随机斜率，DAY固定截距：LMM.model3 = lmer(PM25 ~ AOD + (0 + AOD|Day) ,
data=LMMexcdata)
* AOD随机斜率，DAY随机截距：LMM.model2 = lmer(PM25 ~ AOD + (1 + AOD|Day) ,
data=LMMexcdata)
* 师姐发来的查看斜率和截距的程序：
sslopef=as.numeric(as.matrix(lme4::fixef(fm1)[2]))
sloper=as.numeric(LMM.model(lme4::ranef(fm1)$Day[,2]))
intersf= as.numeric(LMM.model(lme4::fixef(fm1)[1]))
intersr=as.numeric(LMM.model(lme4::ranef(fm1)$Day[,1]))
lme4::fixef(yourmodle)读取固定截距和斜率
lme4::fixef(yourmodle)读取随机截距和斜率
文档中示例（A very basic tutorial for performing linear mixed effects analyses）：
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
#load data into R
politeness=read.csv("http://www.bodowinter.com/tutorial/politeness_data.csv")
#================view the dataset======================
#show the head of politeness
head(politeness)
#show the tail of politeness
tail(politeness)
# other commands you may use
summary(politeness)
str(politeness)
colnames(politeness)
#================check for missing values======================
which(!complete.cases(politeness))
#======look at the relationship between politeness and pitch by means of a
boxplot==========
boxplot(frequency ~ attitude*gender,
col=c("white","lightgray"),politeness)
#================A random intercept model======================
library(Matrix)
library(lme4)
lmer(frequency ~ attitude, data=politeness)
politeness.model = lmer(frequency ~ attitude +
gender + (1|subject) +
(1|scenario), data=politeness)
summary(politeness.model)
#Statistical significance test
politeness.null = lmer(frequency ~ gender +
(1|subject) + (1|scenario), data=politeness,
REML=FALSE)
politeness.model = lmer(frequency ~ attitude +
gender + (1|subject) + (1|scenario),
data=politeness, REML=FALSE)
anova(politeness.null,politeness.model)
#look at the coefficients of the model by subject and by item
coef(politeness.model)
#================A random slope model======================
politeness.model = lmer(frequency ~ attitude +
gender + (1+attitude|subject) +
(1+attitude|scenario),
data=politeness,
REML=FALSE)
coef(politeness.model)
#Statistical significance test (try to obtain a p-value)
#construct the null model
politeness.null = lmer(frequency ~ gender +
(1+attitude|subject) + (1+attitude|scenario),
data=politeness, REML=FALSE)
#do the likelihood ratio test
anova(politeness.null,politeness.model)
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
结果分析
1.使用数据：subject（F1,F2,F3,M3,M4,M7)，gender（M，F），scenario 语境
（1～7），attitude（inf，pol），frequency（e.g.200Hz）
2.随机截距模型：
2.1 代码
politeness.model = lmer(frequency ~ attitude + gender + (1|subject) +
(1|scenario), data=politeness, REML=FALSE)
其中：
Fix effect: attitude, gender（固定斜率）
Random intercepts: subject, scenario （随机截距）
＊we’ve told the model with “(1|subject)” and “(1|scenario)” to take by-subject
and by-item variability into account.
2.2 输出系数分析：（注：这个系数是总系数，固定系数和随机系数已加和）
－－－－－－－－－－－－－－－－－－－－
PS. 若想分别查看固定系数和随机系数，使用以下命令
#输出固定效应系数
print(lme4::fixef(yourmodel))
#输出随机效应系数
print(lme4::ranef(yourmodel))
－－－－－－－－－－－－－－－－－－
对于随机截距模型：
Random intercepts:
scenario1～7：各自具有不同的随机截距
subject（F1,F2,F3,M3,M4,M7)：各自具有不同的随机截距
Fix effect:
对于所有项都是相同的：attitudepol ：attitudepol的pol斜率
genderM：geder的M斜率
3.随机截距模型＋随机截距模型
3.1 代码
politeness.model = lmer(frequency ~ attitude + gender + (1+attitude|subject)
+ (1+attitude|scenario), data=politeness, REML=FALSE)
其中：
> Fix effect:
gender为固定斜率，
> Radom effect:
让attitude随机斜率，
subject，scenario为随机截距
＊The notation “(1+attitude|subject)” means that you tell the model to expect
differing baseline-levels of frequency (the intercept, represented by 1)
3.2 输出系数分析：（注：这个系数是总系数，固定系数和随机系数已加和）
> Fix effect:
genderM：geder的M斜率,固定斜率
> Random intercepts:
scenario1～7：各自具有不同的随机截距
subject（F1,F2,F3,M3,M4,M7)：各自具有不同的随机截距
attitudepol ：attitudepol的pol斜率,随机斜率
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
自己写的程序：
（读取nc文件并合并，做混合效应模型＋系数验证）
#========Set the working directory (on a Mac) and load the data========
##setwd("/Users/Gewanru/Documents/mix effect/")
#=======Read Data from a folder(循环读入多个txt文件）==========
##a = list.files("input")
##dir = paste("./input/",a,sep="")
##n = length(dir)
##LMMexcdata = read.table(file = dir[1],header=TRUE,dec = ".")
##for (i in 2:n){
## new.data = read.table(file = dir[i], header=TRUE, dec = ".")
## LMMexcdata = rbind(LMMexcdata,new.data)
##}
#read a single table
##LMMexcdata <- read.table(file = "merge.txt", header = TRUE, dec = ".")
#========view the data set（查看数据结构）=============
#see the variable names of the data
##names(LMMexcdata)
#show the head of the data
##head(LMMexcdata)
#show the data structure
##str(LMMexcdata)
#check for missing values（misiing value:"NA")
##which(!complete.cases(LMMexcdata))
#show the tail of the data
##tail(LMMexcdata)
# other commands may use
##summary(LMMexcdata)
##colnames(LMMexcdata)
#==========Read nc files（读取气象nc文件，若不用则用上一个读取方式）===============
setwd("/Users/Gewanru/Documents/mix effect/2015/Resultsnc")
library(ncdf4)
ncname <- "0101"
ncfname <- paste(ncname, ".nc", sep = "")
dname <- "PM25"
#===open a NetCDF file==
ncin <- nc_open(ncfname)
print(ncin) #Obtain some basic information of the nc file
#===Read the data from a variable in the file==
PM25data <- ncvar_get(ncin)
nc_close(ncin)
dim(PM25data)#show the the size of the array
print(PM25)
#=======Drawing some plots=============
#Scatter plot(散点图)
##x <- LMMexcdata$AOD #define x lab
##y <- LMMexcdata$PM25 #define y lab
##plot(x, y, main = "Title", xlab = "PM2.5", ylab = "AOD") # "" : mian title &
Title of x(y)lab
#Box plot(箱线图)
#
#====================Correlation（求相关）=========================
#(Here we need to use all of the data)
#correlation
x <- LMMexcdata[,c("PM25","AOD")]
y <- LMMexcdata[,c("PM25","AOD")]
cor(x,y)
#correlation & Significance test（问题1:怎么让输出的数据位数更多一点？）
library(mnormt)
library(psych)
x <- LMMexcdata[,c("PM25","AOD")]
y <- LMMexcdata[,c("PM25","AOD")]
corr.test(x,y,use = "complete")
#===================== Linear Modle （线性回归模型）=====================
#The simplest modle(without temporal and spatial variations)
LMsimplest.model = lm(PM25 ~ AOD , data=LMMexcdata)
summary(LMsimplest.model)
coef(LMsimplest.model)
#Get the coefficient of the Linear Modle
#c1 <- LMsimplest.model$coefficient
#===========Linear Mixed effects model （混合效应模型）===================
#1.(Without site effect)
library(Matrix)
library(lme4)
LMM.model = lmer(PM25 ~ AOD + (1 + AOD|Day) , data=LMMexcdata)
summary(LMM.model)
coef(LMM.model)
print(lme4::fixef(LMM.model))
print(lme4::ranef(LMM.model))
#2.(With site effect)
##LMMsite.model = lmer(PM25 ~ AOD + (1 + AOD|Day) + (1|Site) , data=LMMexcdata)
##summary(LMMsite.model)
##coef(LMMsite.model)
#输出固定效应系数
##print(lme4::fixef(LMMsite.model))
#输出随机效应系数
##print(lme4::ranef(LMMsite.model))
#============Significance test of the model（混合效应模型显著性检验）============
LMM.null1 = lmer(PM25 ~ AOD + (0 + AOD|Day) , data=LMMexcdata, REML=FALSE)
LMM.null2 = lmer(PM25 ~ AOD + (1|Day) , data=LMMexcdata, REML=FALSE)
LMM.model = lmer(PM25 ~ AOD + (1 + AOD|Day) , data=LMMexcdata,REML=FALSE)
anova(LMM.null1,LMM.model)
anova(LMM.null2,LMM.model)
#============ Output (如果需要把系数输出成文本 ，自己完善下代码) ================
#Linear Mixed effects modle
#Get the coefficient of LLM
# coefficient (fixed)
AODslopefix=as.numeric((lme4::fixef(LMM.model)[2]))
interceptfix=as.numeric(as.matrix(lme4::fixef(LMM.model)[1]))
# coefficient (radom)
AODsloperad=as.numeric(as.matrix(lme4::ranef(LMM.model)$Day[,2]))
interceptsrad=as.numeric(as.matrix(lme4::ranef(LMM.model)$Day[,1]))
print(AODslopefix)
print(interceptfix)
print(AODsloperad)
print(interceptsrad)
#==============================================================
