OpenMx (version 2.21.13)

LongitudinalOverdispersedCounts: Longitudinal, Overdispersed Count Data

Description

Four-timepoint longitudinal data generated from an arbitrary Monte Carlo simulation, for 1000 simulees. The response variable is a discrete count variable. There are three time-invariant covariates. The data are available in both "wide" and "long" format.

Usage

data("LongitudinalOverdispersedCounts")

Format

The "long" format dataframe, longData, has 4000 rows and the following variables (columns):

1. id: Factor; simulee ID code.

2. tiem: Numeric; represents the time metric, wave of assessment.

3. x1: Numeric; time-invariant covariate.

4. x2: Numeric; time-invariant covariate.

5. x3: Numeric; time-invariant covariate.

6. y: Numeric; the response ("dependent") variable.

The "wide" format dataset, wideData, is a numeric 1000x12 matrix containing the following variables (columns):

1. id: Simulee ID code.

2. x1: Time-invariant covariate.

3. x3: Time-invariant covariate.

4. x3: Time-invariant covariate.

5. y0: Response at initial wave of assessment.

6. y1: Response at first follow-up.

7. y2: Response at second follow-up.

8. y3: Response at third follow-up.

9. t0: Time variable at initial wave of assessment (in this case, 0).

10. t1: Time variable at first follow-up (in this case, 1).

11. t2: Time variable at second follow-up (in this case, 2).

12. t3: Time variable at third follow-up (in this case, 3).

Examples

data(LongitudinalOverdispersedCounts)
head(wideData)
str(longData)
#Let's try ordinary least-squares (OLS) regression:
olsmod <- lm(y~tiem+x1+x2+x3, data=longData)
#We will see in the diagnostic plots that the residuals are poorly approximated by normality, 
#and are heteroskedastic.  We also know that the residuals are not independent of one another, 
#because we have repeated-measures data:
plot(olsmod)
#In the summary, it looks like all of the regression coefficients are significantly different 
#from zero, but we know that because the assumptions of OLS regression are violated that 
#we should not trust its results:
summary(olsmod)

#Let's try a generalized linear model (GLM).  We'll use the quasi-Poisson quasilikelihood 
#function to see how well the y variable is approximated by a Poisson distribution 
#(conditional on time and covariates):
glm.mod <- glm(y~tiem+x1+x2+x3, data=longData, family="quasipoisson")
#The estimate of the dispersion parameter should be about 1.0 if the data are 
#conditionally Poisson.  We can see that it is actually greater than 2, 
#indicating overdispersion:
summary(glm.mod)