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. 2008 Aug 15;27(18):3643-55.
doi: 10.1002/sim.3210.

Use of log-skew-normal distribution in analysis of continuous data with a discrete component at zero

High Seng Chai  1 , Kent R Bailey
Affiliations

Use of log-skew-normal distribution in analysis of continuous data with a discrete component at zero

High Seng Chai et al. Stat Med. .

Abstract

The problem of analyzing a continuous variable with a discrete component is addressed within the framework of the mixture model proposed by Moulton and Halsey (Biometrics 1995; 51:1570-1578). The model can be generalized by the introduction of the log-skew-normal distribution for the continuous component, and the fit can be significantly improved by its use, while retaining the interpretation of regression parameter estimates. Simulation studies and application to a real data set are used for demonstration.

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Figures

Figure 1
Figure 1
Histograms of the coronary artery calcification (CAC) scores with observed values shown as symbols on the horizontal axis. The bin in gray corresponds to the zero CAC scores.
Figure 2
Figure 2
Histograms of the logarithm of the positive coronary artery calcification (CAC) scores with superimposed fitted densities from various models. The observed values are shown as symbols on the horizontal axis. The shaded bin corresponds to left-censored observations.
Figure 3
Figure 3
Estimated densities based on the Monte Carlo estimates of 1000 simulated data. True value of q is 2 in Scenario 1 and is 0.5 in Scenario 2.
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