library(foreign)
library(lme4)
## Loading required package: Matrix
library(rockchalk)
setwd("/Users/yahyaalshehri/Desktop/PhD Courses/Multilevel Modeling/mlmus3 2")
dta <- read.dta("wheeze.dta")
rockchalk::summarize(dta)
## Numeric variables
## id var smoking y age
## min 1 2 0 0 -2
## med 269 3.50 0 0 -0.50
## max 537 5 1 1 1
## mean 269 3.50 0.35 0.15 -0.50
## sd 155.05 1.12 0.48 0.36 1.12
## skewness 0 0 0.64 1.94 0
## kurtosis -1.20 -1.36 -1.60 1.76 -1.36
## nobs 2148 2148 2148 2148 2148
## nmissing 0 0 0 0 0
head(dta)
## id var smoking y age
## 1 1 2 0 0 -2
## 2 1 3 0 0 -1
## 3 1 4 0 0 0
## 4 1 5 0 0 1
## 5 2 2 0 0 -2
## 6 2 3 0 0 -1
### the first model:
dicotomous.logistic.regression <- glm(y ~ age + smoking, family = binomial, data = dta)
summary(dicotomous.logistic.regression)
##
## Call:
## glm(formula = y ~ age + smoking, family = binomial, data = dta)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6685 -0.5909 -0.5608 -0.5045 2.0613
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.88373 0.08384 -22.467 <2e-16 ***
## age -0.11341 0.05408 -2.097 0.0360 *
## smoking 0.27214 0.12347 2.204 0.0275 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1829.1 on 2147 degrees of freedom
## Residual deviance: 1819.9 on 2145 degrees of freedom
## AIC: 1825.9
##
## Number of Fisher Scoring iterations: 4
##### the second model
Variance.Componant.dicotomous.logistic.regression <- glmer(y ~ 1+ (1|id), family = binomial, data = dta)
summary(Variance.Componant.dicotomous.logistic.regression)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: y ~ 1 + (1 | id)
## Data: dta
##
## AIC BIC logLik deviance df.resid
## 1602.8 1614.2 -799.4 1598.8 2146
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.1991 -0.1604 -0.1604 -0.1604 2.1547
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 5.43 2.33
## Number of obs: 2148, groups: id, 537
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.1161 0.2412 -12.92 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##### the third model
Rando.intercept.dicotomous.logistic.regression <- glmer(y ~ age + smoking + (1|id), family = binomial, data = dta)
summary(Rando.intercept.dicotomous.logistic.regression)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: y ~ age + smoking + (1 | id)
## Data: dta
##
## AIC BIC logLik deviance df.resid
## 1597.9 1620.6 -794.9 1589.9 2144
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.4027 -0.1802 -0.1577 -0.1321 2.5176
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 5.49 2.343
## Number of obs: 2148, groups: id, 537
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.37395 0.27498 -12.270 <2e-16 ***
## age -0.17676 0.06797 -2.601 0.0093 **
## smoking 0.41478 0.28704 1.445 0.1485
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) age
## age 0.227
## smoking -0.419 -0.010