R: Longitudinal, Overdispersed Count Data

LongitudinalOverdispersedCounts {OpenMx} | R Documentation

## 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)

[Package OpenMx version 2.18.1 Index]