Use of medical services in Chile: How sensitive are the results to different econometric models?

Background: We compared different econometric specifications to model the use of medical services in Chile, focussing on visits to general practitioners and specialist physicians. Methods: The evaluated models are the Poisson, Negative Binomial, Zero Inflated Poisson and Negative Binomial, two-step Hurdle model, sample-selection Poisson, and Latent Class model. These models were estimated using Chilean data for the years 2009 and 2015, separated by gender. Results: Unlike previous literature that supported the use of the latent class model, our results show that the latent class model is not always the model with the best goodness of fit. Furthermore, the model with the best fit is not necessarily the model with the best predictive power. For instance, depending on the year and medical services, either the latent class model or the sample-selection Poisson model performs better than the other models. The results also show that the selection of the econometric model may have implications for the estimated influence that variables such as age, income, or affiliation to the public versus private sector have on the use of medical services. Conclusion: Using Chilean data, we have tested that the selection of an econometric method to model the use of medical services is not a problem with a unique answer. We recommend performing a sensitivity analysis of goodness of fit and predictive power between gender, healthcare services, or different years of datasets in future applications to be sure about the best model specification in each context

Nonparametric Identification of Multivariate Mixtures

This article analyzes the identifiability of k-variate, M-component finite mixture models in which each component distribution has independent marginals, including models in latent class analysis. Without making parametric assumptions on the component distributions, we investigate how one can identify the number of components and the component distributions from the distribution function of the observed data. We reveal an important link between the number of variables (k), the number of values each variable can take, and the number of identifiable components. A lower bound on the number of components (M) is nonparametrically identifiable if k >= 2, and the maximum identifiable number of components is determined by the number of different values each variable takes. When M is known, the mixing proportions and the component distributions are nonparametrically identified from matrices constructed from the distribution function of the data if (i) k >= 3, (ii) two of k variables take at least M different values, and (iii) these matrices satisfy some rank and eigenvalue conditions. For the unknown M case, we propose an algorithm that possibly identifies M and the component distributions from data. We discuss a condition for nonparametric identi fication and its observable implications. In case M cannot be identified, we use our identification condition to develop a procedure that consistently estimates a lower bound on the number of components by estimating the rank of a matrix constructed from the distribution function of observed variables.finite mixture, latent class analysis, latent class model, model selection, number of components, rank estimation

Bayesian latent class models for the multiple imputation of categorical data

Latent class analysis has beer recently proposed for the multiple imputation (MI) of missing categorical data, using either a standard frequentist approach or a nonparametric Bayesian model called Dirichlet process mixture of multinomial distributions (DPMM). The main advantage of using a latent class model for multiple imputation is that it is very flexible in the sense that it car capture complex relationships in the data given that the number of latent classes is large enough. However, the two existing approaches also have certain disadvantages. The frequentist approach is computationally demanding because it requires estimating many LC models: first models with different number of classes should be estimated to determine the required number of classes and subsequently the selected model is reestimated for multiple bootstrap samples to take into account parameter uncertainty during the imputation stage. Whereas the Bayesian. Dirichlet process models perform the model selection and the handling of the parameter uncertainty automatically, the disadvantage of this method is that it tends to use a too small number of clusters during the Gibbs sampling, leading to an underfitting model yielding invalid imputations. In this paper, we propose an alternative approach which combined the strengths of the two existing approaches; that is, we use the Bayesian standard latent class model as an imputation model. We show how model selection can be performed prior to the imputation step using a single run of the Gibbs sampler and, moreover, show how underfitting is prevented by using large values for the hyperparameters of the mixture weights. The results of two simulation studies and one real-data study indicate that with a proper setting of the prior distributions, the Bayesian latent class model yields valid imputations and outperforms competing methods

Link Prediction via Generalized Coupled Tensor Factorisation

This study deals with the missing link prediction problem: the problem of predicting the existence of missing connections between entities of interest. We address link prediction using coupled analysis of relational datasets represented as heterogeneous data, i.e., datasets in the form of matrices and higher-order tensors. We propose to use an approach based on probabilistic interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor Factorisation, which can simultaneously fit a large class of tensor models to higher-order tensors/matrices with com- mon latent factors using different loss functions. Numerical experiments demonstrate that joint analysis of data from multiple sources via coupled factorisation improves the link prediction performance and the selection of right loss function and tensor model is crucial for accurately predicting missing links

A new three-step method for using inverse propensity weighting with latent class analysis

Bias-adjusted three-step latent class analysis (LCA) is widely popular to relate covariates to class membership. However, if the causal effect of a treatment on class membership is of interest and only observational data is available, causal inference techniques such as inverse propensity weighting (IPW) need to be used. In this article, we extend the bias-adjusted three-step LCA to incorporate IPW. This approach separates the estimation of the measurement model from the estimation of the treatment effect using IPW only for the later step. Compared to previous methods, this solves several conceptual issues and more easily facilitates model selection and the use of multiple imputation. This new approach, implemented in the software Latent GOLD, is evaluated in a simulation study and its use is illustrated using data of prostate cancer patients