vasishth

nsim<-100000
sd_est<-width<-rep(NA,nsim)
for(i in 1:nsim){
y<-rnorm(10)
sd_est[i]<-sd(y)
ci<-t.test(y)$conf.int
width[i]<-ci[2]-ci[1]
}

plot(width,sd_est)

vasishth

## Load library:
library("exams")

## exam questions:
myexamlist<-list("pnorm1","sesamplesize1multiplechoice")

## output directory
## create new test dir if one does not exist:
files.list<-system("ls",intern=TRUE)

vasishth

library(lme4)
## load data
hindi10<-read.table("datacode/hindi10a.txt",header=TRUE)

## skipping: 1 if word is skipped, 0 otherwise
skip<-ifelse(hindi10$TFT==0,1,0)
hindi10$skip<-skip

summary(hindi10$word_complex)
## make a sum contrast for illustration

vasishth

> # Calculate the predicted random effects by hand for the ergoStool data
> (fm1<-lmer(effort~Type-1 + (1|Subject),ergoStool))
Linear mixed model fit by REML 
Formula: effort ~ Type - 1 + (1 | Subject) 
   Data: ergoStool 
 AIC BIC logLik deviance REMLdev
 133 143  -60.6      122     121
Random effects:
 Groups   Name        Variance Std.Dev.
 Subject  (Intercept) 1.78     1.33    

vasishth

\documentclass[10pt,a4paper]{article}

%% packages
\usepackage{a4wide,verbatim,Sweave,url}

%% new environments
\newenvironment{question}{\item \textbf{Problem}\newline}{}
\newenvironment{solution}{\textbf{Solution}\newline}{}
\newenvironment{answerlist}{\renewcommand{\labelenumi}{(\alph{enumi})}\begin{enumerate}}{\end{enumerate}}

vasishth

\documentclass[10pt,a4paper]{article}

%% packages
\usepackage{a4wide,verbatim,Sweave,url}

%% new environments
\newenvironment{question}{\item}{}
\newenvironment{solution}{\comment}{\endcomment}
\newenvironment{answerlist}{\renewcommand{\labelenumi}{(\alph{enumi})}\begin{enumerate}}{\end{enumerate}}

vasishth

<<echo=FALSE, results=hide>>=
## DATA GENERATION
mean.val<-round(rnorm(1,mean=100,sd=10),digits=0)
sd.val<-round(abs(rnorm(1,mean=10,sd=10)),digits=0)
n<-round(abs(rnorm(1,mean=100,sd=10)),digits=0)+1

se1<-round(sd.val/sqrt(n),digits=3)
se2<-round(sd.val/sqrt(n^2),digits=3)

questions <- character(5)

vasishth

<<echo=FALSE, results=hide>>=
## DATA GENERATION
mean.val<-round(rnorm(1,mean=100,sd=100),digits=0)
sd.val<-round(rnorm(1,mean=100,sd=10),digits=0)

upper<-round(rnorm(1,mean=100,sd=100)+50,digits=0)
lower<-round(rnorm(1,mean=100,sd=100)-100,digits=0)

sol<-pnorm(upper,mean=abs(mean.val),sd=abs(sd.val))-pnorm(lower,mean=abs(mean.val),sd=abs(sd.val))
sol<-round(sol,digits=3)

vasishth

data {
int<lower=1> N;
real rt[N];                         //outcome
real c1[N];                         //predictor
real c2[N];                         //predictor
real c3[N];                         //predictor
int<lower=1> I;                     //number of subjects
int<lower=1, upper=I> id[N];        //subject id
vector[4] mu_prior;                 //vector of zeros passed in from R
}

vasishth

Details:

key:
beta[1] = Intercept
beta[2] = c1
beta[3] = c2
beta[4] = c3

1. Fixed effects, Stan vs lmer:
Stan: