Description Usage Format Examples

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.

1 | ```
data("LongitudinalOverdispersedCounts")
``` |

The "long" format dataframe, `longData`

, has 4000 rows and the following variables (columns):

`id`

: Factor; simulee ID code.`tiem`

: Numeric; represents the time metric, wave of assessment.`x1`

: Numeric; time-invariant covariate.`x2`

: Numeric; time-invariant covariate.`x3`

: Numeric; time-invariant covariate.`y`

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

The "wide" format dataset, `wideData`

, is a numeric 1000x12 matrix containing the following variables (columns):

`id`

: Simulee ID code.`x1`

: Time-invariant covariate.`x3`

: Time-invariant covariate.`x3`

: Time-invariant covariate.`y0`

: Response at initial wave of assessment.`y1`

: Response at first follow-up.`y2`

: Response at second follow-up.`y3`

: Response at third follow-up.`t0`

: Time variable at initial wave of assessment (in this case, 0).`t1`

: Time variable at first follow-up (in this case, 1).`t2`

: Time variable at second follow-up (in this case, 2).`t3`

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
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)
``` |

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