

Nonstandard finite mixture 

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How can I fit a nonstandard mixture (one component is a continuous distribution (skewed to the right) and the other component is a degenerate distribution with mass one at Y=0)? This is what I have tried. In SAS I logtransformed the nonnegative variable by first replacing the original zeros by 0.001 (I called it Z1). Then, in Mplus I tried a twoclass model where one class should have mean log(0.001) and ZERO variance and the other class a normal distribution N(mu,sigma_square). VARIABLE: NAMES = Y1Y4 Z1; USEVARIABLES = Z1; CLASSES = C(2); ANALYSIS: TYPE = MIXTURE; MODEL: %OVERALL% %C#1% !Intercept fixed at log(0.001) [Z1@6.9]; !Zero variance. I GET AN ERROR MESSAGE Z1@0; !INSTEAD (RUNS & I GET RIGHT ANSWER): !Z1@0.00001; Is there other way I could avoid the error message? Or how do I fit this nonstandard distribution in Mplus? 


You could fix the variance at the small value you chose in order to avoid a zero normal variance. I think you can also as an alternative consider a censoredinflated model with censoring at zero. This is a 2class model with one class being zeroonly people and the other class following a censorednormal distribution. Finally, you might consider a twopart model. All these are described in the User's Guide. 


Thanks for your response. I have considered the censoredinflated model with censoring at zero but since the response is strictly nonnegative I have a hard time justifying that it is censored at zero (because it is censored at UNKNOWN tau>0). I want the censoring point to be a parameter and hence to be different from the KNOWN "inflation point" 0. In other words, some of the observed zeros are "true zeros" (class of zeroonly people) and other are "random zeros" (censored at unknown tau>0). I have also tried the twopart model but I am interested in modeling the marginal distribution of Y not the conditional distribution of YY>0. 

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