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Journal articles on the topic 'Latent Covariates'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Mäkikangas, Anne, Asko Tolvanen, Kaisa Aunola, Taru Feldt, Saija Mauno, and Ulla Kinnunen. "Multilevel Latent Profile Analysis With Covariates." Organizational Research Methods 21, no. 4 (February 22, 2018): 931–54. http://dx.doi.org/10.1177/1094428118760690.

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Latent profile analysis (LPA) is a person-centered method commonly used in organizational research to identify homogeneous subpopulations of employees within a heterogeneous population. However, in the case of nested data structures, such as employees nested in work departments, multilevel techniques are needed. Multilevel LPA (MLPA) enables adequate modeling of subpopulations in hierarchical data sets. MLPA enables investigation of variability in the proportions of Level 1 profiles across Level 2 units, and of Level 2 latent classes based on the proportions of Level 1 latent profiles and Level 1 ratings, and the extent to which covariates drawn from the different hierarchical levels of the data affect the probability of a membership of a particular profile. We demonstrate the use of MLPA by investigating job characteristics profiles based on the job-demand-control-support (JDCS) model using data from 1,958 university employees clustered in 78 work departments. The implications of the results for organizational research are discussed, together with several issues related to the potential of MLPA for wider application.

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2

Poon, Wai-Yin, and Hai-Bin Wang. "Latent variable models with ordinal categorical covariates." Statistics and Computing 22, no. 5 (October 12, 2011): 1135–54. http://dx.doi.org/10.1007/s11222-011-9290-8.

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3

Lagishetty, Chakradhar V., Carolyn V. Coulter, and Stephen B. Duffull. "Design of pharmacokinetic studies for latent covariates." Journal of Pharmacokinetics and Pharmacodynamics 39, no. 1 (December 10, 2011): 87–97. http://dx.doi.org/10.1007/s10928-011-9231-3.

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Schofield, Lynne Steuerle, Brian Junker, Lowell J. Taylor, and Dan A. Black. "Predictive Inference Using Latent Variables with Covariates." Psychometrika 80, no. 3 (September 18, 2014): 727–47. http://dx.doi.org/10.1007/s11336-014-9415-z.

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5

Ferrari, Diogo. "Modeling Context-Dependent Latent Effect Heterogeneity." Political Analysis 28, no. 1 (May 20, 2019): 20–46. http://dx.doi.org/10.1017/pan.2019.13.

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Classical generalized linear models assume that marginal effects are homogeneous in the population given the observed covariates. Researchers can never be sure a priori if that assumption is adequate. Recent literature in statistics and political science have proposed models that use Dirichlet process priors to deal with the possibility of latent heterogeneity in the covariate effects. In this paper, we extend and generalize those approaches and propose a hierarchical Dirichlet process of generalized linear models in which the latent heterogeneity can depend on context-level features. Such a model is important in comparative analyses when the data comes from different countries and the latent heterogeneity can be a function of country-level features. We provide a Gibbs sampler for the general model, a special Gibbs sampler for gaussian outcome variables, and a Hamiltonian Monte Carlo within Gibbs to handle discrete outcome variables. We demonstrate the importance of accounting for latent heterogeneity with a Monte Carlo exercise and with two applications that replicate recent scholarly work. We show how Simpson’s paradox can emerge in the empirical analysis if latent heterogeneity is ignored and how the proposed model can be used to estimate heterogeneity in the effect of covariates.

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Li, Ming, and Jeffrey R. Harring. "Investigating Approaches to Estimating Covariate Effects in Growth Mixture Modeling: A Simulation Study." Educational and Psychological Measurement 77, no. 5 (June 15, 2016): 766–91. http://dx.doi.org/10.1177/0013164416653789.

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Researchers continue to be interested in efficient, accurate methods of estimating coefficients of covariates in mixture modeling. Including covariates related to the latent class analysis not only may improve the ability of the mixture model to clearly differentiate between subjects but also makes interpretation of latent group membership more meaningful. Very few studies have been conducted that compare the performance of various approaches to estimating covariate effects in mixture modeling, and fewer yet have considered more complicated models such as growth mixture models where the latent class variable is more difficult to identify. A Monte Carlo simulation was conducted to investigate the performance of four estimation approaches: (1) the conventional three-step approach, (2) the one-step maximum likelihood (ML) approach, (3) the pseudo class (PC) approach, and (4) the three-step ML approach in terms of their ability to recover covariate effects in the logistic regression class membership model within a growth mixture modeling framework. Results showed that when class separation was large, the one-step ML approach and the three-step ML approach displayed much less biased covariate effect estimates than either the conventional three-step approach or the PC approach. When class separation was poor, estimation of the relation between the dichotomous covariate and latent class variable was severely affected when the new three-step ML approach was used.

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Nguyen, Trang Quynh, and Elizabeth A. Stuart. "Propensity Score Analysis With Latent Covariates: Measurement Error Bias Correction Using the Covariate’s Posterior Mean, aka the Inclusive Factor Score." Journal of Educational and Behavioral Statistics 45, no. 5 (April 8, 2020): 598–636. http://dx.doi.org/10.3102/1076998620911920.

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We address measurement error bias in propensity score (PS) analysis due to covariates that are latent variables. In the setting where latent covariate X is measured via multiple error-prone items W, PS analysis using several proxies for X—the W items themselves, a summary score (mean/sum of the items), or the conventional factor score (i.e., predicted value of X based on the measurement model)—often results in biased estimation of the causal effect because balancing the proxy (between exposure conditions) does not balance X. We propose an improved proxy: the conditional mean of X given the combination of W, the observed covariates Z, and exposure A, denoted [Formula: see text]. The theoretical support is that balancing [Formula: see text] (e.g., via weighting or matching) implies balancing the mean of X. For a latent X, we estimate [Formula: see text] by the inclusive factor score (iFS)—predicted value of X from a structural equation model that captures the joint distribution of [Formula: see text] given Z. Simulation shows that PS analysis using the iFS substantially improves balance on the first five moments of X and reduces bias in the estimated causal effect. Hence, within the proxy variables approach, we recommend this proxy over existing ones. We connect this proxy method to known results about valid weighting/matching functions. We illustrate the method in handling latent covariates when estimating the effect of out-of-school suspension on risk of later police arrests using National Longitudinal Study of Adolescent to Adult Health data.

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Zhang, Ningshan, and Jeffrey S. Simonoff. "Joint latent class trees: A tree-based approach to modeling time-to-event and longitudinal data." Statistical Methods in Medical Research 31, no. 4 (February 18, 2022): 719–52. http://dx.doi.org/10.1177/09622802211055857.

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In this paper, we propose a semiparametric, tree-based joint latent class model for the joint behavior of longitudinal and time-to-event data. Existing joint latent class approaches are parametric and can suffer from high computational cost. The most common parametric approach, the joint latent class model, further restricts analysis to using time-invariant covariates in modeling survival risks and latent class memberships. The proposed tree method (joint latent class tree) is fast to fit, and permits time-varying covariates in all of its modeling components. We demonstrate the prognostic value of using time-varying covariates, and therefore the advantage of joint latent class tree over joint latent class model on simulated data. We apply joint latent class tree to a well-known data set (the PAQUID data set) and confirm its superior prediction performance and orders-of-magnitude speedup over joint latent class model.

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9

Alhadabi, Amal. "Latent Heterogeneity in High School Academic Growth: A Comparison of the Performance of Growth Mixture Model, Structural Equation Modeling Tree, and Forest." Journal of Educational and Psychological Studies [JEPS] 16, no. 4 (November 30, 2022): 355–472. http://dx.doi.org/10.53543/jeps.vol16iss4pp355-472.

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The Growth Mixture Model (GMM) is associated with several class enumeration issues. The contemporary advancement of automated algorithms presents two promising alternatives that merge confirmatory Structural Equation Modeling (SEM) with exploratory data-mining algorithms: SEM Tree and SEM Forest. This study investigated the performance of the aforementioned three methods (i.e., the GMM, SEM Tree, and SEM Forest) to detect latent heterogeneity in academic growth across four high school grades using an illustrative subsample of the Longitudinal Study of High School of 2009. The findings showed remarkable differences in detecting latent heterogeneity across the three methods as indicated by a parsimonious number of classes, with more unique growth trajectories, capturing the latent heterogeneity in the growth factors. In contrast, SEM Tree and SEM Forest were better at tracking the influences of covariates in the model parameters’ heterogeneity, as indicated by providing more accurate measures of covariate importance and a detailed description of the role of covariates at each level of the tree or the forest. These findings imply the complementary use of these methods to obtain a clear separation between growth trajectories, as estimated by GMM; and the inclusion of most influential covariates, as identified by SEM Tree and Forest (208 words).

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Alhadabi, Amal. "Latent Heterogeneity in High School Academic Growth: A Comparison of the Performance of Growth Mixture Model, Structural Equation Modeling Tree, and Forest." Journal of Educational and Psychological Studies [JEPS] 16, no. 4 (December 4, 2022): 355–72. http://dx.doi.org/10.53543/jeps.vol16iss4pp355-372.

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The Growth Mixture Model (GMM) is associated with several class enumeration issues. The contemporary advancement of automated algorithms presents two promising alternatives that merge confirmatory Structural Equation Modeling (SEM) with exploratory data-mining algorithms: SEM Tree and SEM Forest. This study investigated the performance of the aforementioned three methods (i.e., the GMM, SEM Tree, and SEM Forest) to detect latent heterogeneity in academic growth across four high school grades using an illustrative subsample of the Longitudinal Study of High School of 2009. The findings showed remarkable differences in detecting latent heterogeneity across the three methods as indicated by a parsimonious number of classes, with more unique growth trajectories, capturing the latent heterogeneity in the growth factors. In contrast, SEM Tree and SEM Forest were better at tracking the influences of covariates in the model parameters’ heterogeneity, as indicated by providing more accurate measures of covariate importance and a detailed description of the role of covariates at each level of the tree or the forest. These findings imply the complementary use of these methods to obtain a clear separation between growth trajectories, as estimated by GMM; and the inclusion of most influential covariates, as identified by SEM Tree and Forest (208 words).

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11

Joo, Jaehyun, Sinead A. Williamson, Ana I. Vazquez, Jose R. Fernandez, and Molly S. Bray. "Advanced Dietary Patterns Analysis Using Sparse Latent Factor Models in Young Adults." Journal of Nutrition 148, no. 12 (November 9, 2018): 1984–92. http://dx.doi.org/10.1093/jn/nxy188.

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ABSTRACT Background Principal components analysis (PCA) has been the most widely used method for deriving dietary patterns to date. However, PCA requires arbitrary ad hoc decisions for selecting food variables in interpreting dietary patterns and does not easily accommodate covariates. Sparse latent factor models can be utilized to address these issues. Objective The objective of this study was to compare Bayesian sparse latent factor models with PCA for identifying dietary patterns among young adults. Methods Habitual food intake was estimated in 2730 sedentary young adults from the Training Interventions and Genetics of Exercise Response (TIGER) Study [aged 18–35 y; body mass index (BMI; in kg/m2): 26.5 ± 6.1] who exercised <30 min/wk during the previous 30 d without restricting caloric intake before study enrollment. A food-frequency questionnaire was used to generate the frequency intakes of 102 food items. Sparse latent factor modeling was applied to the standardized food intakes to derive dietary patterns, incorporating additional covariates (sex, race/ethnicity, and BMI). The identified dietary patterns via sparse latent factor modeling were compared with the PCA derived dietary patterns. Results Seven dietary patterns were identified in both PCA and sparse latent factor analysis. In contrast to PCA, the sparse latent factor analysis allowed the covariate information to be jointly accounted for in the estimation of dietary patterns in the model and offered probabilistic criteria to determine the foods relevant to each dietary pattern. The derived patterns from both methods generally described common dietary behaviors. Dietary patterns 1–4 had similar food subsets using both statistical approaches, but PCA had smaller sets of foods with more cross-loading elements between the 2 factors. Overall, the sparse latent factor analysis produced more interpretable dietary patterns, with fewer of the food items excluded from all patterns. Conclusion Sparse latent factor models can be useful in future studies of dietary patterns by reducing the intrinsic arbitrariness involving the choice of food variables in interpreting dietary patterns and incorporating covariates in the assessment of dietary patterns.

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Choi, Jungsoon, and Andrew B. Lawson. "Bayesian spatially dependent variable selection for small area health modeling." Statistical Methods in Medical Research 27, no. 1 (June 16, 2016): 234–49. http://dx.doi.org/10.1177/0962280215627184.

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Statistical methods for spatial health data to identify the significant covariates associated with the health outcomes are of critical importance. Most studies have developed variable selection approaches in which the covariates included appear within the spatial domain and their effects are fixed across space. However, the impact of covariates on health outcomes may change across space and ignoring this behavior in spatial epidemiology may cause the wrong interpretation of the relations. Thus, the development of a statistical framework for spatial variable selection is important to allow for the estimation of the space-varying patterns of covariate effects as well as the early detection of disease over space. In this paper, we develop flexible spatial variable selection approaches to find the spatially-varying subsets of covariates with significant effects. A Bayesian hierarchical latent model framework is applied to account for spatially-varying covariate effects. We present a simulation example to examine the performance of the proposed models with the competing models. We apply our models to a county-level low birth weight incidence dataset in Georgia.

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Bartolucci, Francesco, Giorgio E. Montanari, and Silvia Pandolfi. "Three-step estimation of latent Markov models with covariates." Computational Statistics & Data Analysis 83 (March 2015): 287–301. http://dx.doi.org/10.1016/j.csda.2014.10.017.

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14

Blozis, Shelley A., and Robert Cudeck. "Conditionally Linear Mixed-Effects Models With Latent Variable Covariates." Journal of Educational and Behavioral Statistics 24, no. 3 (September 1999): 245–70. http://dx.doi.org/10.3102/10769986024003245.

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A version of the nonlinear mixed-effects model is presented that allows random effects only on the linear coefficients. Nonlinear parameters are not stochastic. In nonlinear regression, this kind of model has been called conditionally linear. As a mixed-effects model, this structure is more flexible than the popular linear mixed-effects model, while being nearly as straightforward to estimate. In addition to the structure for the repeated measures, a latent variable model ( Browne, 1993 ) is specified for a distinct set of covariates that are related to the random effects in the second level. Unbalanced data are allowed on the repeated measures, and data that are missing at random are allowed on the repeated measures or on the observed variables of the factor analysis sub-model. Features of the model are illustrated by two examples.

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Blozis, Shelley A., and Robert Cudeck. "Conditionally Linear Mixed-Effects Models with Latent Variable Covariates." Journal of Educational and Behavioral Statistics 24, no. 3 (1999): 245. http://dx.doi.org/10.2307/1165324.

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16

Cai, B., A. B. Lawson, M. M. Hossain, and J. Choi. "Bayesian latent structure models with space-time dependent covariates." Statistical Modelling 12, no. 2 (April 1, 2012): 145–64. http://dx.doi.org/10.1177/1471082x1001200202.

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17

Di Mari, Roberto, Daniel L. Oberski, and Jeroen K. Vermunt. "Bias-Adjusted Three-Step Latent Markov Modeling With Covariates." Structural Equation Modeling: A Multidisciplinary Journal 23, no. 5 (June 17, 2016): 649–60. http://dx.doi.org/10.1080/10705511.2016.1191015.

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18

Forcina, Antonio. "Identifiability of extended latent class models with individual covariates." Computational Statistics & Data Analysis 52, no. 12 (August 2008): 5263–68. http://dx.doi.org/10.1016/j.csda.2008.04.030.

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19

Pearl, Judea. "Detecting Latent Heterogeneity." Sociological Methods & Research 46, no. 3 (August 27, 2015): 370–89. http://dx.doi.org/10.1177/0049124115600597.

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We address the task of determining, from statistical averages alone, whether a population under study consists of several subpopulations, unknown to the investigator, each responding to a given treatment markedly differently. We show that such determination is feasible in three cases: (1) randomized trials with binary treatments, (2) models where treatment effects can be identified by adjustment for covariates, and (3) models in which treatment effects can be identified by mediating instruments. In each of these cases, we provide an explicit condition which, if confirmed empirically, proves that treatment effect is not uniform but varies appreciably across individuals.

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McKennan, Chris, and Dan Nicolae. "Accounting for unobserved covariates with varying degrees of estimability in high-dimensional biological data." Biometrika 106, no. 4 (September 16, 2019): 823–40. http://dx.doi.org/10.1093/biomet/asz037.

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Summary An important phenomenon in high-throughput biological data is the presence of unobserved covariates that can have a significant impact on the measured response. When these covariates are also correlated with the covariate of interest, ignoring or improperly estimating them can lead to inaccurate estimates of and spurious inference on the corresponding coefficients of interest in a multivariate linear model. We first prove that existing methods to account for these unobserved covariates often inflate Type I error for the null hypothesis that a given coefficient of interest is zero. We then provide alternative estimators for the coefficients of interest that correct the inflation, and prove that our estimators are asymptotically equivalent to the ordinary least squares estimators obtained when every covariate is observed. Lastly, we use previously published DNA methylation data to show that our method can more accurately estimate the direct effect of asthma on DNA methylation levels compared to existing methods, the latter of which likely fail to recover and account for latent cell type heterogeneity.

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Lan, Wei, Yue Ding, Zheng Fang, and Kuangnan Fang. "Testing covariates in high dimension linear regression with latent factors." Journal of Multivariate Analysis 144 (February 2016): 25–37. http://dx.doi.org/10.1016/j.jmva.2015.10.013.

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Vermunt, Jeroen K. "Latent Class Modeling with Covariates: Two Improved Three-Step Approaches." Political Analysis 18, no. 4 (2010): 450–69. http://dx.doi.org/10.1093/pan/mpq025.

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Researchers using latent class (LC) analysis often proceed using the following three steps: (1) an LC model is built for a set of response variables, (2) subjects are assigned to LCs based on their posterior class membership probabilities, and (3) the association between the assigned class membership and external variables is investigated using simple cross-tabulations or multinomial logistic regression analysis. Bolck, Croon, and Hagenaars (2004) demonstrated that such a three-step approach underestimates the associations between covariates and class membership. They proposed resolving this problem by means of a specific correction method that involves modifying the third step. In this article, I extend the correction method of Bolck, Croon, and Hagenaars by showing that it involves maximizing a weighted log-likelihood function for clustered data. This conceptualization makes it possible to apply the method not only with categorical but also with continuous explanatory variables, to obtain correct tests using complex sampling variance estimation methods, and to implement it in standard software for logistic regression analysis. In addition, a new maximum likelihood (ML)—based correction method is proposed, which is more direct in the sense that it does not require analyzing weighted data. This new three-step ML method can be easily implemented in software for LC analysis. The reported simulation study shows that both correction methods perform very well in the sense that their parameter estimates and their SEs can be trusted, except for situations with very poorly separated classes. The main advantage of the ML method compared with the Bolck, Croon, and Hagenaars approach is that it is much more efficient and almost as efficient as one-step ML estimation.

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Stoel, Reinoud D., Godfried van den Wittenboer, and Joop Hox. "Including Time-Invariant Covariates in the Latent Growth Curve Model." Structural Equation Modeling: A Multidisciplinary Journal 11, no. 2 (April 2004): 155–67. http://dx.doi.org/10.1207/s15328007sem1102_1.

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Ren, Chunfeng, and Yongyun Shin. "Longitudinal latent variable models given incompletely observed biomarkers and covariates." Statistics in Medicine 35, no. 26 (July 4, 2016): 4729–45. http://dx.doi.org/10.1002/sim.7022.

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Payne, R. D., N. Guha, Y. Ding, and B. K. Mallick. "A conditional density estimation partition model using logistic Gaussian processes." Biometrika 107, no. 1 (December 5, 2019): 173–90. http://dx.doi.org/10.1093/biomet/asz064.

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Summary Conditional density estimation seeks to model the distribution of a response variable conditional on covariates. We propose a Bayesian partition model using logistic Gaussian processes to perform conditional density estimation. The partition takes the form of a Voronoi tessellation and is learned from the data using a reversible jump Markov chain Monte Carlo algorithm. The methodology models data in which the density changes sharply throughout the covariate space, and can be used to determine where important changes in the density occur. The Markov chain Monte Carlo algorithm involves a Laplace approximation on the latent variables of the logistic Gaussian process model which marginalizes the parameters in each partition element, allowing an efficient search of the approximate posterior distribution of the tessellation. The method is consistent when the density is piecewise constant in the covariate space or when the density is Lipschitz continuous with respect to the covariates. In simulation and application to wind turbine data, the model successfully estimates the partition structure and conditional distribution.

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Zhang, Yongxia, Qi Wang, and Maozai Tian. "Smoothed Quantile Regression with Factor-Augmented Regularized Variable Selection for High Correlated Data." Mathematics 10, no. 16 (August 15, 2022): 2935. http://dx.doi.org/10.3390/math10162935.

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This paper studies variable selection for the data set, which has heavy-tailed distribution and high correlations within blocks of covariates. Motivated by econometric and financial studies, we consider using quantile regression to model the heavy-tailed distribution data. Considering the case where the covariates are high dimensional and there are high correlations within blocks, we use the latent factor model to reduce the correlations between the covariates and use the conquer to obtain the estimators of quantile regression coefficients, and we propose a consistency strategy named factor-augmented regularized variable selection for quantile regression (Farvsqr). By principal component analysis, we can obtain the latent factors and idiosyncratic components; then, we use both as predictors instead of the covariates with high correlations. Farvsqr transforms the problem from variable selection with highly correlated covariates to that with weakly correlated ones for quantile regression. Variable selection consistency is obtained under mild conditions. Simulation study and real data application demonstrate that our method is better than the common regularized M-estimation LASSO.

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Hubin, Aliaksandr, Geir O. Storvik, Paul E. Grini, and Melinka A. Butenko. "A Bayesian Binomial Regression Model with Latent Gaussian Processes for Modelling DNA Methylation." Austrian Journal of Statistics 49, no. 4 (April 13, 2020): 46–56. http://dx.doi.org/10.17713/ajs.v49i4.1124.

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Epigenetic observations are represented by the total number of reads from a given pool of cells and the number of methylated reads, making it reasonable to model this data by a binomial distribution. There are numerous factors that can influence the probability of success in a particular region. Moreover, there is a strong spatial (alongside the genome) dependence of these probabilities. We incorporate dependence on the covariates and the spatial dependence of the methylation probability for observations from a pool of cells by means of a binomial regression model with a latent Gaussian field and a logit link function. We apply a Bayesian approach including prior specifications on model configurations. We run a mode jumping Markov chain Monte Carlo algorithm (MJMCMC) across different choices of covariates in order to obtain the joint posterior distribution of parameters and models. This also allows finding the best set of covariates to model methylation probability within the genomic region of interest and individual marginal inclusion probabilities of the covariates.

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Durante, Daniele, Antonio Canale, and Tommaso Rigon. "A nested expectation–maximization algorithm for latent class models with covariates." Statistics & Probability Letters 146 (March 2019): 97–103. http://dx.doi.org/10.1016/j.spl.2018.10.015.

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Thomas, Neal. "The role of secondary covariates when estimating latent trait population distributions." Psychometrika 67, no. 1 (March 2002): 33–48. http://dx.doi.org/10.1007/bf02294708.

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Park, Seohee, Seongeun Kim, and Ji Hoon Ryoo. "Latent Class Regression Utilizing Fuzzy Clusterwise Generalized Structured Component Analysis." Mathematics 8, no. 11 (November 20, 2020): 2076. http://dx.doi.org/10.3390/math8112076.

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Latent class analysis (LCA) has been applied in many research areas to disentangle the heterogeneity of a population. Despite its popularity, its estimation method is limited to maximum likelihood estimation (MLE), which requires large samples to satisfy both the multivariate normality assumption and local independence assumption. Although many suggestions regarding adequate sample sizes were proposed, researchers continue to apply LCA with relatively smaller samples. When covariates are involved, the estimation issue is encountered more. In this study, we suggest a different estimating approach for LCA with covariates, also known as latent class regression (LCR), using a fuzzy clustering method and generalized structured component analysis (GSCA). This new approach is free from the distributional assumption and stable in estimating parameters. Parallel to the three-step approach used in the MLE-based LCA, we extend an algorithm of fuzzy clusterwise GSCA into LCR. This proposed algorithm has been demonstrated with an empirical data with both categorical and continuous covariates. Because the proposed algorithm can be used for a relatively small sample in LCR without requiring a multivariate normality assumption, the new algorithm is more applicable to social, behavioral, and health sciences.

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Böckenholt, Ulf, and William R. Dillon. "Inferring Latent Brand Dependencies." Journal of Marketing Research 37, no. 1 (February 2000): 72–87. http://dx.doi.org/10.1509/jmkr.37.1.72.18726.

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In this article, the authors develop a class of models to reconstruct brand-transition probabilities when individual brand purchase sequence information is not available. The authors introduce two general model forms by assuming different underlying mechanisms for individual heterogeneity in brand switching. The first model form captures individual heterogeneity by a latent class structure. The second model form captures individual heterogeneity by postulating that the brand-choice probabilities follow a Dirichlet distribution, which yields the popular Dirichlet multinomial formulation. Monte Carlo simulations are performed with a view toward assessing whether individual transition probabilities can be captured from knowledge of only aggregated brand choices. Results indicate that the proposed method can indeed capture individual brand-transition probabilities under several different conditions. An empirical application illustrates how these models can be used to provide important information on individual brand transitions and the role of marketing-related covariates.

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Song, Xin-Yuan, and Sik-Yum Lee. "Bayesian Analysis of Structural Equation Models With Nonlinear Covariates and Latent Variables." Multivariate Behavioral Research 41, no. 3 (September 2006): 337–65. http://dx.doi.org/10.1207/s15327906mbr4103_4.

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Rutkowski, Leslie, and Yan Zhou. "Correcting Measurement Error in Latent Regression Covariates via the MC-SIMEX Method." Journal of Educational Measurement 52, no. 4 (November 2015): 359–75. http://dx.doi.org/10.1111/jedm.12090.

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Martinez, Edson Zangiacomi, Jorge Alberto Achcar, and Francisco Louzada-Neto. "Bayesian Estimation of Diagnostic Tests Accuracy for Semi-Latent Data with Covariates." Journal of Biopharmaceutical Statistics 15, no. 5 (September 1, 2005): 809–21. http://dx.doi.org/10.1081/bip-200067912.

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Wiesner, Margit, and Michael Windle. "Assessing Covariates of Adolescent Delinquency Trajectories: A Latent Growth Mixture Modeling Approach." Journal of Youth and Adolescence 33, no. 5 (October 2004): 431–42. http://dx.doi.org/10.1023/b:joyo.0000037635.06937.13.

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Forcina, Antonio. "A Fisher-scoring algorithm for fitting latent class models with individual covariates." Econometrics and Statistics 3 (July 2017): 132–40. http://dx.doi.org/10.1016/j.ecosta.2016.07.001.

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Joo, Seang-Hwane, Philseok Lee, and Stephen Stark. "The Explanatory Generalized Graded Unfolding Model: Incorporating Collateral Information to Improve the Latent Trait Estimation Accuracy." Applied Psychological Measurement 46, no. 1 (October 11, 2021): 3–18. http://dx.doi.org/10.1177/01466216211051717.

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Collateral information has been used to address subpopulation heterogeneity and increase estimation accuracy in some large-scale cognitive assessments. The methodology that takes collateral information into account has not been developed and explored in published research with models designed specifically for noncognitive measurement. Because the accurate noncognitive measurement is becoming increasingly important, we sought to examine the benefits of using collateral information in latent trait estimation with an item response theory model that has proven valuable for noncognitive testing, namely, the generalized graded unfolding model (GGUM). Our presentation introduces an extension of the GGUM that incorporates collateral information, henceforth called Explanatory GGUM. We then present a simulation study that examined Explanatory GGUM latent trait estimation as a function of sample size, test length, number of background covariates, and correlation between the covariates and the latent trait. Results indicated the Explanatory GGUM approach provides scoring accuracy and precision superior to traditional expected a posteriori (EAP) and full Bayesian (FB) methods. Implications and recommendations are discussed.

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von Davier, Matthias, and Sandip Sinharay. "Stochastic Approximation Methods for Latent Regression Item Response Models." Journal of Educational and Behavioral Statistics 35, no. 2 (April 2010): 174–93. http://dx.doi.org/10.3102/1076998609346970.

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This article presents an application of a stochastic approximation expectation maximization (EM) algorithm using a Metropolis-Hastings (MH) sampler to estimate the parameters of an item response latent regression model. Latent regression item response models are extensions of item response theory (IRT) to a latent variable model with covariates serving as predictors of the conditional distribution of ability. Applications to estimating latent regression models for National Assessment of Educational Progress (NAEP) data from the 2000 Grade 4 mathematics assessment and the Grade 8 reading assessment from 2002 are presented and results of the proposed method are compared to results obtained using current operational procedures.

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Bartolucci, Francesco, and Antonio Forcina. "A Class of Latent Marginal Models for Capture–Recapture Data With Continuous Covariates." Journal of the American Statistical Association 101, no. 474 (June 1, 2006): 786–94. http://dx.doi.org/10.1198/073500105000000243.

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Guerra-Peña, Kiero, and Douglas Steinley. "Extracting Spurious Latent Classes in Growth Mixture Modeling With Nonnormal Errors." Educational and Psychological Measurement 76, no. 6 (July 11, 2016): 933–53. http://dx.doi.org/10.1177/0013164416633735.

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Growth mixture modeling is generally used for two purposes: (1) to identify mixtures of normal subgroups and (2) to approximate oddly shaped distributions by a mixture of normal components. Often in applied research this methodology is applied to both of these situations indistinctly: using the same fit statistics and likelihood ratio tests. This can lead to the overextraction of latent classes and the attribution of substantive meaning to these spurious classes. The goals of this study are (1) to explore the performance of the Bayesian information criterion, sample-adjusted BIC, and bootstrap likelihood ratio test in growth mixture modeling analysis with nonnormal distributed outcome variables and (2) to examine the effects of nonnormal time invariant covariates in the estimation of the number of latent classes when outcome variables are normally distributed. For both of these goals, we will include nonnormal conditions not considered previously in the literature. Two simulation studies were conducted. Results show that spurious classes may be selected and optimal solutions obtained in the data analysis when the population departs from normality even when the nonnormality is only present in time invariant covariates.

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Lowe, Patricia A. "Examination of Latent Test Anxiety Profiles in a Sample of U.S. Adolescents." International Education Studies 14, no. 2 (January 25, 2021): 12. http://dx.doi.org/10.5539/ies.v14n2p12.

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The present study examined latent test anxiety profiles in a sample of 592 U.S. adolescents in grades 6-12 using latent profile analysis (LPA). The adolescents were administered a multidimensional measure of test anxiety in their schools. The results of LPA indicated that a three-profile test anxiety model provided the best fitting model. The three latent test anxiety subgroups were named low, medium, and high test anxiety. In addition, grade-level and gender were added as covariates to the model and LPA was performed again. Grade-level and gender were found to differentially predict membership in the latent test anxiety subgroups, with females more likely to be in the high latent test anxiety subgroup than in the medium and low latent test anxiety subgroups and middle school students were more likely to be in the high latent test anxiety subgroup than in the low latent test anxiety subgroup. Middle school students were also more likely to be in the medium latent test anxiety subgroup than in the low latent test anxiety subgroup. Implications for the development of measures, treatment, and prevention of test anxiety in the U.S. adolescent population are discussed.

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Bakk, Zsuzsa, Roberto Di Mari, Jennifer Oser, and Jouni Kuha. "Two-stage Multilevel Latent Class Analysis with Covariates in the Presence of Direct Effects." Structural Equation Modeling: A Multidisciplinary Journal 29, no. 2 (October 20, 2021): 267–77. http://dx.doi.org/10.1080/10705511.2021.1980882.

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Sun, Xuxue, Wenjun Cai, and Mingyang Li. "A hierarchical modeling approach for degradation data with mixed-type covariates and latent heterogeneity." Reliability Engineering & System Safety 216 (December 2021): 107928. http://dx.doi.org/10.1016/j.ress.2021.107928.

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Humphreys, Keith, and Harald Janson. "Latent Transition Analysis with Covariates, Nonresponse, Summary Statistics and Diagnostics: Modelling Children's Drawing Development." Multivariate Behavioral Research 35, no. 1 (January 2000): 89–118. http://dx.doi.org/10.1207/s15327906mbr3501_4.

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Montanari, Giorgio E., and Silvia Pandolfi. "Evaluation of long-term health care services through a latent Markov model with covariates." Statistical Methods & Applications 27, no. 1 (August 24, 2017): 151–73. http://dx.doi.org/10.1007/s10260-017-0390-2.

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Vermunt, Jeroen K., Rolf Langeheine, and Ulf Bockenholt. "Discrete-Time Discrete-State Latent Markov Models with Time-Constant and Time-Varying Covariates." Journal of Educational and Behavioral Statistics 24, no. 2 (June 1999): 179–207. http://dx.doi.org/10.3102/10769986024002179.

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Vermunt, Jeroen K., Rolf Langeheine, and Ulf Bockenholt. "Discrete-Time Discrete-State Latent Markov Models with Time-Constant and Time-Varying Covariates." Journal of Educational and Behavioral Statistics 24, no. 2 (1999): 179. http://dx.doi.org/10.2307/1165200.

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Gudicha, Dereje W., Verena D. Schmittmann, and Jeroen K. Vermunt. "Statistical power of likelihood ratio and Wald tests in latent class models with covariates." Behavior Research Methods 49, no. 5 (December 30, 2016): 1824–37. http://dx.doi.org/10.3758/s13428-016-0825-y.

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Lee, Sik-Yum, Xin-Yuan Song, and Nian-Sheng Tang. "Bayesian Methods for Analyzing Structural Equation Models With Covariates, Interaction, and Quadratic Latent Variables." Structural Equation Modeling: A Multidisciplinary Journal 14, no. 3 (July 31, 2007): 404–34. http://dx.doi.org/10.1080/10705510701301511.

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Harring, Jeffrey R., Nidhi Kohli, Rebecca D. Silverman, and Deborah L. Speece. "A Second-Order Conditionally Linear Mixed Effects Model With Observed and Latent Variable Covariates." Structural Equation Modeling: A Multidisciplinary Journal 19, no. 1 (January 20, 2012): 118–36. http://dx.doi.org/10.1080/10705511.2012.634729.

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