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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 log-transformed the non-negative variable by first replacing the original zeros by 0.001 (I called it Z1). Then, in Mplus I tried a two-class 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 = Y1-Y4 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? |
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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 censored-inflated model with censoring at zero. This is a 2-class model with one class being zero-only people and the other class following a censored-normal distribution. Finally, you might consider a two-part model. All these are described in the User's Guide. |
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Thanks for your response. I have considered the censored-inflated model with censoring at zero but since the response is strictly non-negative 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 zero-only people) and other are "random zeros" (censored at unknown tau>0). I have also tried the two-part model but I am interested in modeling the marginal distribution of Y not the conditional distribution of Y|Y>0. |
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