Homework 8 Part 1 Random Effect Slides

The Comparison Between Two Types of Random Interaction Models

Model 1

In this model you are doing a cross level interaction between gender differences and teachers years experience while at the same time randomly looking at gender differences between schools.

#cross level interaction between sex and teachers years experience
m4_lme <- lme(popular ~ sex*texp, data = popula, random = ~ sex|school, method = "ML")
summary(m4_lme)

Linear mixed-effects model fit by maximum likelihood
 Data: popula 
      AIC      BIC    logLik
  4261.85 4306.657 -2122.925

Random effects:
 Formula: ~sex | school
 Structure: General positive-definite, Log-Cholesky parametrization
            StdDev    Corr  
(Intercept) 0.6347377 (Intr)
sex         0.4692521 0.08  
Residual    0.6264320       

Fixed effects: popular ~ sex * texp 
                Value  Std.Error   DF   t-value p-value
(Intercept)  3.313651 0.15954654 1898 20.769180   0e+00
sex          1.329479 0.13183479 1898 10.084432   0e+00
texp         0.110229 0.01013882   98 10.872007   0e+00
sex:texp    -0.034025 0.00837995 1898 -4.060303   1e-04
 Correlation: 
         (Intr) sex    texp  
sex      -0.046              
texp     -0.909  0.042       
sex:texp  0.042 -0.908 -0.046

Standardized Within-Group Residuals:
        Min          Q1         Med          Q3         Max 
-2.93387434 -0.64733763  0.02294381  0.53272602  3.49150352 

Number of Observations: 2000
Number of Groups: 100 

Model 2 Centering Covariates

In the second model we are doing the same with the exception of mutating the variable teachers years experience to center around zero. Doing this helps us interpret the intercept. We are centering the constant from every value of the variable which in this case is teachers experience.

popula %<>% mutate(ctexp = texp - mean(texp))

m4a_lme <- lme(popular ~ sex*ctexp, data = popula, random = ~ sex|school, method = "ML")
summary(m4a_lme)

Linear mixed-effects model fit by maximum likelihood
 Data: popula 
      AIC      BIC    logLik
  4261.85 4306.657 -2122.925

Random effects:
 Formula: ~sex | school
 Structure: General positive-definite, Log-Cholesky parametrization
            StdDev    Corr  
(Intercept) 0.6347377 (Intr)
sex         0.4692521 0.08  
Residual    0.6264320       

Fixed effects: popular ~ sex * ctexp 
                Value  Std.Error   DF  t-value p-value
(Intercept)  4.885851 0.06660875 1898 73.35149   0e+00
sex          0.844178 0.05510824 1898 15.31855   0e+00
ctexp        0.110229 0.01013882   98 10.87201   0e+00
sex:ctexp   -0.034025 0.00837995 1898 -4.06030   1e-04
 Correlation: 
          (Intr) sex    ctexp 
sex       -0.044              
ctexp     -0.006  0.000       
sex:ctexp  0.000 -0.004 -0.046

Standardized Within-Group Residuals:
        Min          Q1         Med          Q3         Max 
-2.93387434 -0.64733763  0.02294381  0.53272602  3.49150352 

Number of Observations: 2000
Number of Groups: 100 

Let’s look at them together:

*Both models show popularity to be highers for girls than boys.

*Teachers experience also seems to increase pupils popularity index.

• Despite the numerical differences in the coefficients, the “story” of the interaction of teachers experience and gender among popularity is still the focuse of the two models.

*Both models work and are perfect fits since they both have the same BIC and AIC results.

htmlreg(list(m4_lme, m4a_lme))

Statistical models

	Model 1	Model 2
(Intercept)	3.31***	4.89***
	(0.16)	(0.07)
sex	1.33***	0.84***
	(0.13)	(0.06)
texp	0.11***
	(0.01)
sex:texp	-0.03***
	(0.01)
ctexp		0.11***
		(0.01)
sex:ctexp		-0.03***
		(0.01)
AIC	4261.85	4261.85
BIC	4306.66	4306.66
Log Likelihood	-2122.92	-2122.92
Num. obs.	2000	2000
Num. groups	100	100
p < 0.001, p < 0.01, p < 0.05