# pnmtrem1.sim.data2:
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

### 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

### 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