Original Paper
Linear Logistic Latent Class Analysis
Abstract
In the present paper the linear logistic extension of latent class analysis is described. Thereby it is assumed that the item latent probabilities as well as the class sizes can be attributed to some explanatory variables. The basic equations of the model state the decomposition of the log‐odds of the item latent probabilities and of the class sizes into weighted sums of basic parameters representing the effects of the predictor variables. Further, the maximum likelihood equations for these effect parameters and statistical tests for goodness‐of‐fit are given. Finally, an example illustrates the practical application of the model and the interpretation of the model parameters.
Citing Literature
Number of times cited according to CrossRef: 27
- Alexander Robitzsch, Regularized Latent Class Analysis for Polytomous Item Responses: An Application to SPM-LS Data, Journal of Intelligence, 10.3390/jintelligence8030030, 8, 3, (30), (2020).
- Naoki Nishimura, Noriyoshi Sukegawa, Yuichi Takano, Jiro Iwanaga, A latent-class model for estimating product-choice probabilities from clickstream data, Information Sciences, 10.1016/j.ins.2017.11.014, 429, (406-420), (2018).
- Ian Hickie, Brian Parsonage, Gordon Parker, Prediction of Response to Electroconvulsive Therapy, British Journal of Psychiatry, 10.1192/bjp.157.1.65, 157, 1, (65-71), (2018).
- A. Felipe, N. Martín, P. Miranda, L. Pardo, Statistical inference in constrained latent class models for multinomial data based on $$\phi $$ ϕ -divergence measures, Advances in Data Analysis and Classification, 10.1007/s11634-017-0289-7, 12, 3, (605-636), (2017).
- Dereje W. Gudicha, Fetene B. Tekle, Jeroen K. Vermunt, Power and Sample Size Computation for Wald Tests in Latent Class Models, Journal of Classification, 10.1007/s00357-016-9199-1, 33, 1, (30-51), (2016).
- ANTON K. FORMANN, THOMAS KOHLMANN, Structural Latent Class Models, Sociological Methods & Research, 10.1177/0049124198026004005, 26, 4, (530-565), (2016).
- Anton K Formann, Thomas Kohlmann, Latent class analysis in medical research, Statistical Methods in Medical Research, 10.1177/096228029600500205, 5, 2, (179-211), (2016).
- Judith A. Holt, George B. Macready, A Simulation Study of the Difference Chi-Square Statistic for Comparing Latent Class Models Under Violation of Regularity Conditions, Applied Psychological Measurement, 10.1177/014662168901300301, 13, 3, (221-231), (2016).
- A. Felipe, P. Miranda, L. Pardo, Minimum $$\phi $$ ϕ -Divergence Estimation in Constrained Latent Class Models for Binary Data, Psychometrika, 10.1007/s11336-015-9450-4, 80, 4, (1020-1042), (2015).
- Anton K. Formann, Latent Class Analysis , Wiley StatsRef: Statistics Reference Online, 10.1002/9781118445112, (2014).
- Anton K. Formann, Measuring Change in Latent Subgroups Using Dichotomous Data: Unconditional, Conditional, and Semiparametric Maximum Likelihood Estimation, Journal of the American Statistical Association, 10.1080/01621459.1994.10476838, 89, 427, (1027-1034), (2012).
- Jing Feng, Wei Yang, Effects of Particulate Air Pollution on Cardiovascular Health: A Population Health Risk Assessment, PLoS ONE, 10.1371/journal.pone.0033385, 7, 3, (e33385), (2012).
- Nicole White, Helen Johnson, Peter Silburn, George Mellick, Nadeeka Dissanayaka, Kerrie Mengersen, Probabilistic subgroup identification using Bayesian finite mixture modelling: A case study in Parkinson's disease phenotype identification, Statistical Methods in Medical Research, 10.1177/0962280210391012, 21, 6, (563-583), (2010).
- Linda M. Collins, Stephanie T. Lanza, Bibliography, Latent Class and Latent Transition Analysis, undefined, (266-278), (2010).
- Alexander Basilevsky, References, Statistical Factor Analysis and Related Methods, undefined, (690-731), (2008).
- Matthias von Davier, Jürgen Rost, 19 Mixture Distribution Item Response Models, Psychometrics, 10.1016/S0169-7161(06)26019-X, (643-661), (2006).
- Gerhard H. Fischer, 16 Rasch Models, Psychometrics, 10.1016/S0169-7161(06)26016-4, (515-585), (2006).
- C. Mitchell Dayton, George B. Macready, 13 Latent Class Analysis in Psychometrics, Psychometrics, 10.1016/S0169-7161(06)26013-9, (421-446), (2006).
- Anton K. Formann, Samuel Kotz, Campbell B. Read, N. Balakrishnan, Brani Vidakovic, Norman L. Johnson, Latent Class Analysis, Encyclopedia of Statistical Sciences, 10.1002/0471667196, (2004).
- Dankmar Böhning, Wilfried Seidel, Editorial: recent developments in mixture models, Computational Statistics & Data Analysis, 10.1016/S0167-9473(02)00161-5, 41, 3-4, (349-357), (2003).
- Anton K. Formann, Latent class model diagnostics—a review and some proposals, Computational Statistics & Data Analysis, 10.1016/S0167-9473(02)00186-X, 41, 3-4, (549-559), (2003).
- Karen Bandeen-roche, Diana L. Miglioretti, Scott L. Zeger, Paul J. Rathouz, Latent Variable Regression for Multiple Discrete Outcomes, Journal of the American Statistical Association, 10.1080/01621459.1997.10473658, 92, 440, (1375-1386), (1997).
- Dankmar Böhning, A review of reliable maximum likelihood algorithms for semiparametric mixture models, Journal of Statistical Planning and Inference, 10.1016/0378-3758(94)00119-G, 47, 1-2, (5-28), (1995).
- Anton K. Formann, Linear Logistic Latent Class Analysis for Polytomous Data, Journal of the American Statistical Association, 10.1080/01621459.1992.10475229, 87, 418, (476-486), (1992).
- C. Mitchell Dayton, George B. Macready, Concomitant-Variable Latent-Class Models, Journal of the American Statistical Association, 10.1080/01621459.1988.10478584, 83, 401, (173-178), (1988).
- Rolf Langeheine, New Developments in Latent Class Theory, Latent Trait and Latent Class Models, 10.1007/978-1-4757-5644-9, (77-108), (1988).
- Clifford C. Clogg, Leo A. Goodman, Latent Structure Analysis of a Set of Multidimensional Contingency Tables, Journal of the American Statistical Association, 10.1080/01621459.1984.10477093, 79, 388, (762-771), (1984).
