Dissertations / Theses on the topic 'Latent Covariates'

Latent variable models (LVMs) are commonly used in the scenario where the outcome of the main interest is an unobservable measure, associated with multiple observed surrogate outcomes, and affected by potential risk factors. This thesis develops an approach of efficient handling missing surrogate outcomes and covariates in two- and three-level latent variable models. However, corresponding statistical methodologies and computational software are lacking efficiently analyzing the LVMs given surrogate outcomes and covariates subject to missingness in the LVMs. We analyze the two-level LVMs for longitudinal data from the National Growth of Health Study where surrogate outcomes and covariates are subject to missingness at any of the levels. A conventional method for efficient handling of missing data is to reexpress the desired model as a joint distribution of variables, including the surrogate outcomes that are subject to missingness conditional on all of the covariates that are completely observable, and estimate the joint model by maximum likelihood, which is then transformed to the desired model. The joint model, however, identifies more parameters than desired, in general. The over-identified joint model produces biased estimates of LVMs so that it is most necessary to describe how to impose constraints on the joint model so that it has a one-to-one correspondence with the desired model for unbiased estimation. The constrained joint model handles missing data efficiently under the assumption of ignorable missing data and is estimated by a modified application of the expectation-maximization (EM) algorithm.

We considered the problem of predicting student retention using logistic regression when the most important covariates such as the college variables are latent, but the network structure is known. This network structure specifies the relationship between pre-college to college variables and then from college to student retention variables. Based on this structure, we developed three estimators, examined their large-sample properties, and evaluated their empirical efficiencies using WKU student retention database. Results show that while the hat estimator is expected to be most efficient, the tilde estimator was shown to be more efficient than the check method. This increased efficiency suggests that utilizing the network information can improve our predictions.

Factor mixture modeling (FMM) has been increasingly used to investigate unobserved population heterogeneity. This Monte Carlo simulation study examined the issue of measurement invariance testing with FMM when there are covariate effects. Specifically, this study investigated the impact of excluding and misspecifying covariate effects on the class enumeration and measurement invariance testing with FMM. Data were generated based on three FMM models where the covariate had impact on the latent class membership only (population model 1), both the latent class membership and the factor (population model 2), and the latent class membership, the factor, and one item (population model 3). The number of latent classes was fixed at two. These two latent classes were distinguished by factor mean difference for conditions where measurement invariance held in the population, and by both factor mean difference and intercept differences across classes when measurement invariance did not hold in the population. For each of the population models, different analysis models that excluded or misspecified covariate effects were fitted to data. Analyses consisted of two parts. First, for each analysis model, class enumeration rates were examined by comparing the fit of seven solutions: 1-class, 2-class configural, metric, and scalar, and 3-class configural, metric, and scalar. Second, assuming the correct solution was selected, the fit of analysis models with the same solution was compared to identify a best-fitting model. Results showed that completely excluding the covariate from the model (i.e., the unconditional model) would lead to under-extraction of latent classes, except when the class separation was large. Therefore, it is recommended to include covariate in FMM when the focus is to identify the number of latent classes and the level of invariance. Specifically, the covariate effect on the latent class membership can be included if there is no priori hypothesis regarding whether measurement invariance might hold or not. Then fit of this model can be compared with other models that included covariate effects in different ways but with the same number of latent classes and the same level of invariance to identify a best-fitting model.

Customer lifetime value (CLV) is a forecasted expectation of the future value of a customer to the firm. There are two customer behavioral components of CLV that represent a particular modeling challenge: 1) how many transactions we expect from a customer in the future, and 2) how likely it is the customer remains active. Existing CLV models like the Pareto/NBD are valuable managerial tools because they are able to provide forward-looking estimates of transaction patterns and customer churn when the event of a customer leaving is unobservable, which is typical for most noncontractual goods and services. The CLV model literature has for the most part maintained its original assumption that the number of customer transactions follows a stable transaction process. Yet there are many categories of noncontractual goods and services where the stable transaction rate assumption is violated, particularly seasonal purchase patterns. CLV model estimates are further biased when there is an excess of customers with no repeat transactions. To address these modeling challenges, within this thesis I develop a generalized CLV modeling framework that combines three elements necessary to reduce bias in model estimates: 1) the incorporation of time-varying covariates to model data with transaction rates that change over time, 2) a zero-inflated model specification for customers with no repeat transactions, and 3) generalizes to different transaction process distributions to better fit diverse customer transaction patterns. This CLV modeling framework provides firms better estimates of the future activity of their customers, a critical CRM application.

The purpose of this paper is to generalize regression models for repeated categorical data based on maximizing a conditional likelihood. Some existing methods, such as those proposed by Duncan (1985), Fischer (1989), and Agresti (1993, and 1997) are special cases of this latent variable approach, used to account for dependencies in clustered observations. The generalization concerns the incorporation of rather general data structures such as subject-specific time-dependent covariates, a variable number of observations per subject and time periods of arbitrary length in order to evaluate treatment effects on a categorical response variable via a linear parameterization. The response may be polytomous, ordinal or dichotomous. The main tool is the log-linear representation of appropriately parameterized Rasch-type models, which can be fitted using standard software, e.g., R. The proposed method is applied to data from a psychiatric study on the evaluation of psychobiological variables in the therapy of depression. The effects of plasma levels of the antidepressant drug Clomipramine and neuroendocrinological variables on the presence or absence of anxiety symptoms in 45 female patients are analyzed. The individual measurements of the time dependent variables were recorded on 2 to 11 occasions. The findings show that certain combinations of the variables investigated are favorable for the treatment outcome. (author´s abstract)
Series: Research Report Series / Department of Statistics and Mathematics

Nous présentons une nouvelle méthode pour étudier les relations entre la structure génétique des populations et l'environnement. Cette méthode repose sur des modèles hiérarchiques bayésiens qui utilisent conjointement des données génétiques multi-locus et des données spatiales, environnementales et/ou culturelles. Elle permet d'estimer la structure génétique des populations, d'évaluer ses liens avec des covariables non génétiques, et de projeter la structure génétique des populations en fonction de ces covariables. Dans un premier temps, nous avons appliqué notre approche à des données de génétique humaine pour évaluer le rôle de la géographie et des langages dans la structure génétique des populations amérindiennes. Dans un deuxième temps, nous avons étudié la structure génétique des populations pour 20 espèces de plantes alpines et nous avons projeté les modifications intra spécifiques qui pourront être causées par le réchauffement climatique
We introduce a new method to study the relationships between population genetic structure and environment. This method is based on Bayesian hierarchical models which use both multi-loci genetic data, and spatial, environmental, and/or cultural data. Our method provides the inference of population genetic structure, the evaluation of the relationships between the structure and non-genetic covariates, and the prediction of population genetic structure based on these covariates. We present two applications of our Bayesian method. First, we used human genetic data to evaluate the role of geography and languages in shaping Native American population structure. Second, we studied the population genetic structure of 20 Alpine plant species and we forecasted intra-specific changes in response to global warming. STAR

We propose the use of Latent Class Analysis methods to analyze the covariate inclusion patterns across specifications resulting from Bayesian model averaging exercises. Using Dirichlet Process clustering, we are able to identify and describe dependency structures among variables in terms of inclusion in the specifications that compose the model space. We apply the method to two datasets of potential determinants of economic growth. Clustering the posterior covariate inclusion structure of the model space formed by linear regression models reveals interesting patterns of complementarity and substitutability across economic growth determinants.

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Financiadora de Estudos e Projetos
The application of a gold standard reference test in all or part of the sample under investigation is often not feasible for the majority of diseases affecting humans, either by a lack of consensus on which testing may be considered a gold standard, the high level of invasion of the gold standard technique, the high cost of financially large-scale application, or by ethical questions, so to know the performance of existing tests is essential for the process of diagnosis of these diseases. In statistical modeling aimed to obtain robust estimates of the prevalence of the disease (x ) and the performance parameters of diagnostic tests (sensitivity (Se) and specificity (Sp)), various strategies have been considered such as the stratification of the population, the relaxation of the assumption of conditional independence, the inclusion of covariates, the verification type (partial or total) and the techniques to replace the gold standard. In this thesis we propose a new structure of stratification of the population considering both the prevalence rates and the parameters of test performance among the different strata (EHW). A Bayesian latent class modeling to estimate these parameters was developed for the general case of K diagnostic tests under investigation, relaxation of the assumption of conditional independence according to the formulations of the fixed effect (FECD) and random (RECD) with dependent order (h _ k) and M covariates. The application of models to two data sets about the performance evaluation of diagnostic tests used in screening for Chagas disease in blood donors showed results consistent with the sensitivity studies. Overall, we observed for the structure of stratification proposal (EHW) superior performance and estimates closer to the nominal values when compared to the structure of stratification when only the prevalence rates are different between the strata (HW), even when we consider data set with rates of Se, Sp and x close among the strata. Generally, the structure of latent class, when we have low or high prevalence of the disease, estimates of sensitivity and specificity rates have higher standard errors. However, in these cases, when there is high concordance of positive or negative results of the tests, the error pattern of these estimates are reduced. Regardless of the structure of stratification (EHW, HW), sample size and the different scenarios used to model the prior information, the model of conditional dependency from the FECD and RECD had, from the information criteria (AIC, BIC and DIC), superior performance to the structure of conditional independence (CI) and to FECD with improved performance and estimates closer to the nominal values. Besides the connection logit, derived from the logistic distribution with symmetrical shape, find in the link GEV, derived from the generalized extreme value distribution which accommodates symmetric and asymmetric shapes, a interesting alternative to construct the conditional dependence structure from the RECD. As an alternative to the problem of identifiability, present in this type of model, the criteria adopted to elicit the informative priors by combining descriptive analysis of data, adjustment models from simpler structures, were able to produce estimates with low standard error and very close to the nominal values.
Na área da saúde a aplicação de teste de referência padrão ouro na totalidade ou parte da amostra sob investigação é, muitas vezes, impraticável devido à inexistência de consenso sobre o teste a ser considerado padrão ouro, ao elevado nível de invasão da técnica, ao alto custo da aplicação em grande escala ou por questões éticas. Contudo, conhecer o desempenho dos testes é fundamental no processo de diagnóstico. Na modelagem estatística voltada à estimação da taxa de prevalência da doença (x ) e dos parâmetros de desempenho de testes diagnósticos (sensibilidade (S) e especificidade (E)), a literatura tem explorado: estratificação da população, relaxamento da suposição de independência condicional, inclusão de covariáveis, tipo de verificação pelo teste padrão ouro e técnicas para substituir o teste padrão ouro inexistente ou inviável de ser aplicado em toda a amostra. Neste trabalho, propomos uma nova estrutura de estratificação da população considerando taxas de prevalências e parâmetros de desempenho diferentes entre os estratos (HWE). Apresentamos uma modelagem bayesiana de classe latente para o caso geral de K testes diagnósticos sob investigação, relaxamento da suposição de independência condicional segundo as formulações de efeito fixo (DCEF) e efeito aleatório (DCEA) com dependência de ordem (h _ K) e inclusão de M covariáveis. A aplicação dos modelos a dois conjuntos de dados sobre avaliação do desempenho de testes diagnósticos utilizados na triagem da doença de Chagas em doadores de sangue apresentou resultados coerentes com os estudos de sensibilidade. Observamos, para a estrutura de estratificação proposta, HWE, desempenho superior e estimativas muito próximas dos valores nominais quando comparados à estrutura de estratificação na qual somente as taxas de prevalências são diferentes entre os estratos (HW), mesmo quando consideramos dados com taxas de S, E e x muito próximas entre os estratos. Geralmente, na estrutura de classe latente, quando temos baixa ou alta prevalência da doença, as estimativas das sensibilidades e especificidades apresentam, respectivamente, erro padrão mais elevado. No entanto, quando há alta concordância de resultados positivos ou negativos, tal erro diminui. Independentemente da estrutura de estratificação (HWE, HW), do tamanho amostral e dos diferentes cenários utilizados para modelar o conhecimento a priori, os modelos de DCEF e de DCEA apresentaram, a partir dos critérios de informação (AIC, BIC e DIC), desempenhos superiores à estrutura de independência condicional (IC), sendo o de DCEF com melhor desempenho e estimativas mais próximas dos valores nominais. Além da ligação logito, derivada da distribuição logística com forma simétrica, encontramos na ligação VEG , derivada da distribuição de valor extremo generalizada a qual acomoda formas simétricas e assimétricas, interessante alternativa para construir a estrutura de DCEA. Como alternativa ao problema de identificabilidade, neste tipo de modelo, os critérios para elicitar as prioris informativas, combinando análise descritiva dos dados com ajuste de modelos de estruturas mais simples, contribuíram para produzir estimativas com baixo erro padrão e muito próximas dos valores nominais.

Educational researchers are often interested in phenomena that unfold over time within a person and at the same time, relationships between their characteristics that are stable over time. Since variables in a longitudinal study reflect both within- and between-person effects, researchers need to disaggregate them to understand the phenomenon of interest correctly. Although the person-mean centering technique has been believed as the gold standard of the disaggregation method, recent studies found that the centering did not work when there was a trend in the predictor. Hence, they proposed some detrending techniques to remove the systematic change; however, they were only applicable to multilevel models. Therefore, this dissertation develops novel detrending methods based on structural equation modeling (SEM). It also establishes the links between centering and detrending by reviewing a broad range of literature. The proposed SEM-based detrending methods are compared to the existing centering and detrending methods through a series of Monte Carlo simulations. The results indicate that (a) model misspecification for the time-varying predictors or outcomes leads to large bias of and standard error, (b) statistical properties of estimates of the within- and between-person effects are mostly determined by the type of between-person predictors (i.e., observed or latent), and (c) for unbiased estimation of the effects, models with latent between-person predictors require nonzero growth factor variances, while those with observed predictors at the between level need either nonzero or zero variance, depending on the parameter. As concluding remarks, some practical recommendations are provided based on the findings of the present study.
Doctor of Philosophy
Educational researchers are often interested in longitudinal phenomena within a person and relations between the person's characteristics. Since repeatedly measured variables reflect their within- and between-person aspects, researchers need to disaggregate them statistically to understand the phenomenon of interest. Recent studies found that the traditional centering method, where the individual's average of a predictor was subtracted from the original predictor value, could not correctly disentangle the within- and between-person effects when the predictor showed a systematic change over time (i.e., trend). They proposed some techniques to remove the trend; however, the detrending methods were only applicable to multilevel models. Therefore, the present study develops novel detrending methods using structural equation modeling. The proposed models are compared to the existing methods through a series of Monte Carlo simulations, where we can manipulate a data-generating model and its parameter values. The results indicate that (a) model misspecification for the time-varying predictor or outcome leads to systematic deviation of the estimates from their true values, (b) statistical properties of estimates of the effects are mostly determined by the type of between-person predictors (i.e., observed or latent), and (c) the latent predictor models require nonzero growth factor variances for unbiased estimation, while the observed predictor models need either nonzero or zero variance, depending on the parameter. As concluding remarks, some recommendations for the practitioners are provided.

Nous présentons une nouvelle méthode pour étudier les relations entre la structure génétique des populations et l'environnement. Cette méthode repose sur des modèles hiérarchiques bayésiens qui utilisent conjointement des données génétiques multi-locus et des données spatiales, environnementales et/ou culturelles. Elle permet d'estimer la structure génétique des populations, d'évaluer ses liens avec des covariables non génétiques, et de projeter la structure génétique des populations en fonction de ces covariables. Dans un premier temps, nous avons appliqué notre approche à des données de génétique humaine pour évaluer le rôle de la géographie et des langages dans la structure génétique des populations amérindiennes. Dans un deuxième temps, nous avons étudié la structure génétique des populations pour 20 espèces de plantes alpines et nous avons projeté les modifications intra spécifiques qui pourront être causées par le réchauffement climatique.

abstract: The purpose of this study was to examine under which conditions "good" data characteristics can compensate for "poor" characteristics in Latent Class Analysis (LCA), as well as to set forth guidelines regarding the minimum sample size and ideal number and quality of indicators. In particular, we studied to which extent including a larger number of high quality indicators can compensate for a small sample size in LCA. The results suggest that in general, larger sample size, more indicators, higher quality of indicators, and a larger covariate effect correspond to more converged and proper replications, as well as fewer boundary estimates and less parameter bias. Based on the results, it is not recommended to use LCA with sample sizes lower than N = 100, and to use many high quality indicators and at least one strong covariate when using sample sizes less than N = 500.
Dissertation/Thesis
M.A. Psychology 2012

A latent class signal detection (SDT) model was recently introduced as an alternative to traditional item response theory (IRT) methods in the analysis of constructed response data. This class of models can be represented as restricted latent class models and differ from the IRT approach in the way the latent construct is conceptualized. One appeal of the signal detection approach is that it provides an intuitive framework from which psychological processes governing rater behavior can be better understood. The present study developed an extension of the latent class SDT model to include covariates and examined the performance of the resulting model. Covariates can be incorporated into the latent class SDT model in three ways: 1) to affect latent class membership, 2) conditional response probabilities and 3) both latent class membership and conditional response probabilities. In each case, simulations were conducted to investigate both parameter recovery and classification accuracy of the extended model under two competing rater designs; in addition, implications of ignoring covariate effects and covariate misspecification were explored. Here, the ability of information criteria, namely the AIC, small sample adjusted AIC and BIC, in recovering the true model with respect to how covariates are introduced was also examined. Results indicate that parameters were generally well recovered in fully-crossed designs; to obtain similar levels of estimation precision in incomplete designs, sample size requirements were comparatively higher and depend on the number of indicators used. When covariate effects were not accounted for or misspecified, results show that parameter estimates tend to be severely biased, which in turn reduced classification accuracy. With respect to model recovery, the BIC performed the most consistently amongst the information criteria considered. In light of these findings, recommendations were made with regard to sample size requirements and model building strategies when implementing the extended latent class SDT model.

Incomplete data often arise in the study of life history processes. Examples include missing responses, missing covariates, and unobservable latent processes in addition to right censoring. This thesis is on the development of statistical models and methods to address these problems as they arise in oncology and chronic disease. Methods of estimation and inference in parametric, weakly parametric and semiparametric settings are investigated. Studies of chronic diseases routinely sample individuals subject to conditions on an event time of interest. In epidemiology, for example, prevalent cohort studies aiming to evaluate risk factors for survival following onset of dementia require subjects to have survived to the point of screening. In clinical trials designed to assess the effect of experimental cancer treatments on survival, patients are required to survive from the time of cancer diagnosis to recruitment. Such conditions yield samples featuring left-truncated event time distributions. Incomplete covariate data often arise in such settings, but standard methods do not deal with the fact that the covariate distribution is also affected by left truncation. We develop a likelihood and algorithm for estimation for dealing with incomplete covariate data in such settings. An expectation-maximization algorithm deals with the left truncation by using the covariate distribution conditional on the selection criterion. An extension to deal with sub-group analyses in clinical trials is described for the case in which the stratification variable is incompletely observed. In studies of affective disorder, individuals are often observed to experience recurrent symptomatic exacerbations of symptoms warranting hospitalization. Interest lies in modeling the occurrence of such exacerbations over time and identifying associated risk factors to better understand the disease process. In some patients, recurrent exacerbations are temporally clustered following disease onset, but cease to occur after a period of time. We develop a dynamic mover-stayer model in which a canonical binary variable associated with each event indicates whether the underlying disease has resolved. An individual whose disease process has not resolved will experience events following a standard point process model governed by a latent intensity. If and when the disease process resolves, the complete data intensity becomes zero and no further events will arise. An expectation-maximization algorithm is developed for parametric and semiparametric model fitting based on a discrete time dynamic mover-stayer model and a latent intensity-based model of the underlying point process. The method is applied to a motivating dataset from a cohort of individuals with affective disorder experiencing recurrent hospitalization for their mental health disorder. Interval-censored recurrent event data arise when the event of interest is not readily observed but the cumulative event count can be recorded at periodic assessment times. Extensions on model fitting techniques for the dynamic mover-stayer model are discussed and incorporate interval censoring. The likelihood and algorithm for estimation are developed for piecewise constant baseline rate functions and are shown to yield estimators with small empirical bias in simulation studies. Data on the cumulative number of damaged joints in patients with psoriatic arthritis are analysed to provide an illustrative application.

博士
國立交通大學
統計學研究所
106
Recently, the regression extension of latent class analysis (RLCA) models have played an important role in many fields of research. RLCA models establish the relationship between primary covariates and latent class membership as well as the mediated direct effect of secondary covariates on measured responses. They have proven helpful for analyzing the relationship between measured multiple responses and covariates of interest. In this paper, we propose a generalized estimating equation (GEE) approach for the parameter estimation of RLCA models. This approach allows the specification of a working covariance that can ease the specification of the true covariance structure. We detail several structures of working covariance, iterative algorithms of Gauss-Newton methods for parameter estimation, and procedures for obtaining covariances of parameter estimators. An analysis of variables that probably affect the frailty of patients with cancer is used for illustration.