# MATH 6643 Summer 2012 Applications of Mixed Models/Students/smithce

## Contents

I am a PhD student in Psychology in the Quantitative Methods Area. I completed my Masters in Psychology degree at York studying depth perception and my undergraduate degree at the University of Toronto in Engineering Science, Aerospace option. As you can see I have quite a varied (and some might say strange) educational background! This year I had the privilege of working as a consultant with the Statistical Consulting Service, which was a fabulous experience.

I have experience working with R, Matlab and SPSS. I am especially fond of R.

## Something Useful

The results of plot for simulate.lme always felt lackluster to me. So I created a new and improved version. I prepared a script with my new function, and demo code at the bottom here.

## Discussion Questions

### Chapter 2

• I once attended an HLM workshop at a large Education conference. A fellow attendee was skeptical of the entire enterprise. In the example provided the within-group, between-group and pooled effects for socio-economic status were all positively and statistically significantly related with the outcome measure. His opinion was, that since all three effects were in the same direction and significant, why bother with the extra complexity, since it would simply confuse the pants off his trustees anyway. How would you respond?
• Post: Consider the macro-micro-micro-macro causal chain (pg. 12, Figure 2.7). What would happen if one were to model this simply as a macro-macro (W -> Z) model, omitting the intermediate variables? What if the true relationship was micro-macro-macro-micro? The potential for errors in causal assumptions have always bothered me, especially in SEM type analyses, but it still applies here. In Psychology we are attributing some meaning to a variable, but it could easily be read another way. Here's a convoluted example: The researcher assumes: Teacher Disciplinarianism -> Student Behaviour -> Student Success -> Teacher Stress. But perhaps the pathways are different, and in fact: Student Behaviour -> Teacher Disciplinarianism -> Teacher Stress -> Student Success.

### Chapter 3

• In the course we use the language of "contextual", "compositional", "between", "within" and "pooled" effects. Identify each from the example on page 28-29 and on the graph Figure 3.4.

### Chapter 4

• Describe the relative advantages and disadvantages of REML and ML estimation. When should you choose one over the other?
• Write an R script to simulate appropriate data and fit Models 3 and 4 from page 70.