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From |
"Bryan W. Griffin" <bwgriffin@GeorgiaSouthern.edu> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Generating correlated binary data |

Date |
Tue, 26 Apr 2005 09:28:39 -0400 |

I am trying to generate correlated binary data to model random effects with xtlogit. I plan to do several Monte Carlo type studies. My question is about the specific form of the data to generate. I have two predictors, x1 (within cluster predictor) and z1 (between cluster predictor), and the outcome will be binary. The model takes this form:

logit(pij) = B0j + B1*x1ij + B2*z1ij

B0j = b0 + u0j

so

logit(pij) = b0 + B1*x1ij + B2*z1ij + u0j

where there are i observations within cluster j.

The issue I have is whether there should be a within-cluster error term added to the model when generating data. That is, should the model to generate binary data appear like this (the .3 appear in the equation because I copy and pasted from code I used, see below)

generate y1_w_error =.3 + .3*x1 +.3*z1 + u0j + e

or like this

generate y1_wo_error =.3 + .3*x1 + .3*z1 + u0j ?

With linear models I know the "e" should be included, and in fact my code below generates data for continuous outcomes that behave well, but I'm uncertain about the logistic case.

My code is listed below.

set obs 30

generate float z1= round(uniform())

generate float u0j= invnorm(uniform())*1.69

generate n = 30

range id2 1 30

expand n

generate float x1= round(uniform())

generate float e= invnorm(uniform())

* Option 1 -- model with level 1 error

generate y1_w_error =.3 + .3*x1 +.3*z1 + u0j + e

generate p_w_error = exp(y1_w_error)/(1+exp(y1_w_error))

generate binary_y_w_error = uniform()<=p_w_error

* Option 2 -- model without level 1 error

generate y1_wo_error =.3 + .3*x1 + .3*z1 + u0j

generate p_wo_error = exp(y1_wo_error)/(1+exp(y1_wo_error))

generate binary_y_wo_error = uniform()<=p_wo_error

___________________________________________________________________

Bryan W. Griffin

Curriculum, Foundations, & Reading

P.O. Box 8144

Georgia Southern University

Statesboro, GA 30460-8144

Phone: 912-681-0488

E-Mail: bwgriffin@GeorgiaSouthern.edu

WWW: http://coe.georgiasouthern.edu/foundations/bwgriffin/

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