A portion of a simulated dataset, for t ≥q 2 period, from a first-order Probit-Normal Marginalized Transition Random Effects Models for 500 subjects with 4 follow-ups

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Description

The dataset includes bivariate longitudinal binary responses and two associated covariates. The first covariate, X1 is a time-independent one which means it takes same values at t=1, 2, 3, 4. For the details of X1, see pnmtrem1.sim.data1. The second covariate, X2 is a response type indicator variable which takes 1 for the first response, and takes 0 for the second one. The assumed parameters to generate the data are: β=(β_0, β_1, β_2) = (-1, 2, 0.2), α_{t,1}=(α_{21,1}, α_{31,1}, α_{41,1})= (0.5, 0.7, 0.9), λ_j=(λ_1, λ_2)=(1, 1.05) and b_{it} \sim N(0,σ_t^2), σ_t=(σ_2, σ_3, σ_4)=(0.66, 0.63, 0.60). It is assumed that there 500 subjects. The dataset has no missing value.

Usage

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Format

A data frame with 3000 observations on the following 7 variables.

time

a numeric vector for the time information at which data is available

response

a numeric vector with the response information for which data is available

subject

a numeric vector for subject id

y

a numeric vector for bivariate longitudinal binary responses

ones

a numeric vector for which all the elements are 1

x1

a numeric vector for the first covariate, X1

x2

a numeric vector for the second covariate, X2

Details

When one carefully investigates the time, response and subject orders, s/he can easily understand the data structure which the model accepts. Baseline and later time points of the data may include different number of independent variables. Therefore, datasets for t=1 and t ≥q 2 are presented in different data objects, pnmtrem1.sim.data1 and pnmtrem1.sim.data2, respectively.

Examples

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