data management
dta$ID <- factor(dta$ID)
dta$Wave <- factor(dta$Wave)
dta$Age2 = dta$Age -6.5 #shifted by 6.5
str(dta)
## 'data.frame': 267 obs. of 6 variables:
## $ ID : Factor w/ 89 levels "1","2","3","4",..: 1 1 1 2 2 2 3 3 3 4 ...
## $ Wave : Factor w/ 3 levels "1","2","3": 1 2 3 1 2 3 1 2 3 1 ...
## $ Age_G: num 6.5 8.5 10.5 6.5 8.5 10.5 6.5 8.5 10.5 6.5 ...
## $ Age : num 6 8.33 10.33 6 8.5 ...
## $ PIAT : int 18 35 59 18 25 28 18 23 32 18 ...
## $ Age2 : num -0.5 1.83 3.83 -0.5 2 ...
head(dta)
## ID Wave Age_G Age PIAT Age2
## 1 1 1 6.5 6.0000 18 -0.5000
## 2 1 2 8.5 8.3333 35 1.8333
## 3 1 3 10.5 10.3333 59 3.8333
## 4 2 1 6.5 6.0000 18 -0.5000
## 5 2 2 8.5 8.5000 25 2.0000
## 6 2 3 10.5 10.5833 28 4.0833
ggplot, Eighty-nine children’s scores on PIAT
library(ggplot2)
p <- ggplot(dta,
aes(Age2, PIAT)) +
geom_line(aes(group=ID), alpha=0.5) +
stat_smooth(aes(group=Age2),
method="lm",
formula= y ~ x) +
geom_point(alpha=0.5) +
labs(x="Age (in years, shifted by 6.5)",
y="PIAT score") +
theme_minimal()
suppressWarnings(suppressMessages(ggplot2:::print.ggplot(p)))
m0
library(lme4)
## Loading required package: Matrix
m0 <- lmer(PIAT ~ Age2 + ( 1 |ID), dta)
summary(m0)
## Linear mixed model fit by REML ['lmerMod']
## Formula: PIAT ~ Age2 + (1 | ID)
## Data: dta
##
## REML criterion at convergence: 1859
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.04325 -0.56799 -0.05908 0.55574 2.88911
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 26.73 5.170
## Residual 44.10 6.641
## Number of obs: 267, groups: ID, 89
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 21.0625 0.8439 24.96
## Age2 4.5411 0.2219 20.46
##
## Correlation of Fixed Effects:
## (Intr)
## Age2 -0.588
sjPlot::tab_model(m0, show.obs=F, show.ngroups=F, show.r2=FALSE, show.re.var=F,show.icc=F, show.se=T)
|
|
PIAT
|
|
Predictors
|
Estimates
|
std. Error
|
CI
|
p
|
|
(Intercept)
|
21.06
|
0.84
|
19.41 – 22.72
|
<0.001
|
|
Age2
|
4.54
|
0.22
|
4.11 – 4.98
|
<0.001
|
m1
m1 <- lmer(PIAT ~ Age2 + ( Age2 |ID), dta)
summary(m1)
## Linear mixed model fit by REML ['lmerMod']
## Formula: PIAT ~ Age2 + (Age2 | ID)
## Data: dta
##
## REML criterion at convergence: 1804.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0042 -0.4893 -0.1383 0.4067 3.6892
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## ID (Intercept) 5.507 2.347
## Age2 3.377 1.838 0.53
## Residual 27.400 5.235
## Number of obs: 267, groups: ID, 89
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 21.0621 0.5630 37.41
## Age2 4.5399 0.2622 17.32
##
## Correlation of Fixed Effects:
## (Intr)
## Age2 -0.288
sjPlot::tab_model(m1, show.obs=F, show.ngroups=F, show.r2=FALSE, show.re.var=F,show.icc=F, show.se=T)
|
|
PIAT
|
|
Predictors
|
Estimates
|
std. Error
|
CI
|
p
|
|
(Intercept)
|
21.06
|
0.56
|
19.96 – 22.17
|
<0.001
|
|
Age2
|
4.54
|
0.26
|
4.03 – 5.05
|
<0.001
|
Compare model
sjPlot::tab_model(m0, m1, show.obs=F, show.ngroups=F, show.r2=T, show.re.var=T,show.icc=T, show.se=T)
|
|
PIAT
|
PIAT
|
|
Predictors
|
Estimates
|
std. Error
|
CI
|
p
|
Estimates
|
std. Error
|
CI
|
p
|
|
(Intercept)
|
21.06
|
0.84
|
19.41 – 22.72
|
<0.001
|
21.06
|
0.56
|
19.96 – 22.17
|
<0.001
|
|
Age2
|
4.54
|
0.22
|
4.11 – 4.98
|
<0.001
|
4.54
|
0.26
|
4.03 – 5.05
|
<0.001
|
|
Random Effects
|
|
σ2
|
44.10
|
27.40
|
|
τ00
|
26.73 ID
|
5.51 ID
|
|
τ11
|
|
3.38 ID.Age2
|
|
ρ01
|
|
0.53 ID
|
|
ICC
|
0.38
|
0.62
|
|
Marginal R2 / Conditional R2
|
0.499 / 0.688
|
0.496 / 0.807
|
anova(m0,m1)
## refitting model(s) with ML (instead of REML)
## Data: dta
## Models:
## m0: PIAT ~ Age2 + (1 | ID)
## m1: PIAT ~ Age2 + (Age2 | ID)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m0 4 1866.9 1881.3 -929.46 1858.9
## m1 6 1815.9 1837.4 -901.95 1803.9 55.021 2 1.128e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
The end