

Simulation of overdispersion in LGM 

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I am MCsimulating overdispersed count data (nb) generated from a quadratic growth curve model of an outcome with 5 timepoints. The specification of the modelimplied outcome variances will result in dispersionparameter values that are equal to the specified variances. Given the restriction of the modelimplied outcome intercepts to zero and the NegBin2 VarianceFunction (mu_i+alpha*mu_i^2) it not obvious to me why this has to happen. Example: Specified: i BY y1y5@1; s BY y1@0 y2@1 y3@2 y4@3 y5@4; q BY y1@0 y2@1 y3@4 y4@9 y5@16; [y1y5*0]; !!!!!!!!!! y1*3.000; !!!!!!!!!! y2*5.000; !!!!!!!!!! y3*5.000; !!!!!!!!!! y4*3.000; !!!!!!!!!! y5*3.000; !!!!!!!!!! [i*0.5 s*0.25 q*0.2]; i*1.0; s*0.2; q*0.01; i WITH s*0.3; i WITH q*0.05; s WITH q*0; Results in: Dispersion Y1 3.000 Y2 5.000 Y3 5.000 Y4 3.000 Y5 3.000 Thank you! 


With a count variable, the name of the count variable refers to the dispersion parameter, alpha, not the variance. So when you say y1*3 you are giving the alpha parameter value. 

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