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We developed a single factor model with measure-specific sample weights formultivariate data with multiple observed indicators clustered within a higherlevel subject. The factor is therefore a latent variable shared by multipleindicators within a same subject and the sample weights are different acrossdifferent indicators and different subjects. Even after integrating out thelatent variable, the likelihood of the data cannot be written as the sum ofweighted likelihood of each subject because a subject has different sampleweights respectively for its multiple indicators. In addition, the number ofavailable indicators varies across subjects. We derive a pseudo likelihood forthe latent variable model with measure-specific weights. We investigate variousstatistical properties of the latent variable model with measure-specificsample weights and its connection to the traditional factor analysis. We foundthat the latent variable model provides consistent estimates for its varianceswhen the measure-specific sample weights are properly re-scaled. Two estimationprocedures are developed - EM algorithm for the pseudo likelihood andmarginalization of the pseudo likelihood by directly integrating out the latentvariable to obtain the parameter estimates. This approach is illustrated by theanalysis of publicly reported hospitals with indicators and sample weights.Numerical studies are conducted to investigate the influence of weights andtheir sample distribution.

Latent Variable Model for Multivariate Data with Measure-specific Sample Weights and Its Application in Hospital Compare