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  • Computation of densities for exemplary observations with Finite Mixture Model (FMM) and Quantil Regression (QR)

    Dear Statalist,

    I want to use a Finite Mixture Model (4 Gaussian's) and a Quantile Regression to compare the distributional fit of those 2 models on a dataset.
    Therefore I want to compare computed densities for exemplary observations of the dataset by
    (1) graphing them (like kdensity but not for the whole dataset, only exemplary observations) and
    (2) by estimating quantiles

    My question is: How can I compute those densities for exemplary observations.

    For QR I would proceed as follows:
    1. run QR for q(1) given the whole dataset
    2. predict xb to get the linear prediction for the first quantile
    3. repeat for quantile 2 to 99 to get the linear prediction for quantiles 2 to 99
    4. plot those values for an exemplary observation

    For FMM I don't know how to proceed. My suggestion would be
    1. run FMM with 4 Gaussian's given the whole dataset to obtain latent class probabilities and estimates conditional on the latent class
    2. due to the underlying assumptions of normal distributions and the estimated latent class probabilites for a given observation, it should somehow be possible to estimate values for the quantiles 1 to 99 for an exemplary observation
    3. plot those values for the same exemplary observation as in 4. above.

    Any help or suggestions are appreciated a lot. If you have any further question which could help in answering my question, don't hesistate to ask.

    Kind regards,

    Steffen Pl├╝tzke