The two models that are below evaluate the Cross-level interaction of variables using two different methods. In this analysis I will be looking into and explaining each method.
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 The first cross level interaction model looks into student perception of popularity by gender. It also looks into teachers experience while looking into the interaction of a school and sex. The fixed effect shows that there is an interaction between gender and teacher experience. The average popularity index for a boy with a teacher that has no experience is 3.31. For every 1 year increase in experience of the teacher boys perception of popularity increases by .11. On average for females their perception of popularity is 4.6 when the teacher has no experience. The random effect for this model examines a random school and says that on average the popularity perception is .63 higher than the fixed effect and females are .46 higher.
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 The second model is a little bit of a different. In the centering of the covariates we have created a new center for the variable making the mean the starting point. We are controlling the outputs and anything below mean will fall below 0 and those above will be higher than 0. It shows that on average males perception of popularity is 4.88 when teacher experience is average. Females perception of popularity is 5.72 when teacher experience is average. When the mean teacher’s experience increases by 1 year boys perception of popularity increases by .11 while females perception decreases by .03. The random effect for this model examines a random school and suggests thaton average the popularity perception is .6347 higher than the fixed effect and females are .4692 higher than 4.64.
library(texreg)
htmlreg(list(m4_lme, m4a_lme))| 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 | |||
The 2 models are similar.The Similarities we can look into is the random effect which demonstrates that a random school’s gender difference has the same difference in either model. Just because there are some numerical differences in the intercepts and slopes the story line of the interaction of teachers experience and gender is still the center of the models. They both examine the interaction of teachers experience with gender to see the influence both variables have together on personal perception of popularity. The differences between both models are the fixed effect calculations but it is different because we have centered the variable teachers experience. This is to control the outliers and to see where gender falls when the mean of teachers experience is the starting point.