Parameter constraints in generalized linear latent variable models

Parameter constraints in generalized linear latent variable models are discussed. Both linear equality and inequality constraints are considered. Maximum likelihood estimators for the parameters of the constrained model and corrected standard errors are derived. A significant reduction in the dimension of the optimization problem is achieved with the proposed methodology for fitting models subject to linear equality constraints.

[1]  Dimitri P. Bertsekas,et al.  Constrained Optimization and Lagrange Multiplier Methods , 1982 .

[2]  D. G. Weeks,et al.  Linear structural equations with latent variables , 1980 .

[3]  M. Knott,et al.  Generalized latent trait models , 2000 .

[4]  Y. Ritov,et al.  Analysis of contingency tables by correspondence models subject to order constraints , 1993 .

[5]  F. T. Wright,et al.  Order restricted statistical inference , 1988 .

[6]  P. Bentler,et al.  A modified Newton method for constrained estimation in covariance structure analysis , 1993 .

[7]  S. Baker Composite linear models for incomplete multinomial data. , 1994, Statistics in medicine.

[8]  G. H. Fischer,et al.  Logistic latent trait models with linear constraints , 1983 .

[9]  Irini Moustaki,et al.  A general class of latent variable models for ordinal manifest variables with covariate effects on the manifest and latent variables. , 2003, The British journal of mathematical and statistical psychology.

[10]  A. Forcina,et al.  A Unified Approach to Likelihood Inference on Stochastic Orderings in a Nonparametric Context , 1998 .

[11]  L. A. Goodman The Analysis of Systems of Qualitative Variables When Some of the Variables Are Unobservable. Part I-A Modified Latent Structure Approach , 1974, American Journal of Sociology.

[12]  R. P. McDonald,et al.  A simple comprehensive model for the analysis of covariance structures: Some remarks on applications , 1980 .

[13]  F. V. D. Pol,et al.  MIXED MARKOV LATENT CLASS MODELS , 1990 .

[14]  Anton K. Formann,et al.  Constrained latent class models: Theory and applications , 1985 .

[15]  L. A. Goodman Exploratory latent structure analysis using both identifiable and unidentifiable models , 1974 .

[16]  Leo A. Goodman,et al.  SIMULTANEOUS LATENT STRUCTURE ANALYSIS IN SEVERAL GROUPS , 1985 .

[17]  Sik-Yum Lee Estimation of covariance structure models with parameters subject to functional restraints , 1980 .

[18]  D. Rindskopf Using phantom and imaginary latent variables to parameterize constraints in linear structural models , 1984 .

[19]  Shelby J. Haberman,et al.  A Stabilized Newton-Raphson Algorithm for Log-Linear Models for Frequency Tables Derived by Indirect Observation , 1988 .

[20]  I. Moustaki,et al.  Generalized latent variable models with non-linear effects. , 2008, The British journal of mathematical and statistical psychology.

[21]  B. Wright,et al.  Best test design , 1979 .

[22]  H. Hoijtink Constrained Latent Class Analysis Using the Gibbs Sampler and Posterior Predictive P-values: Applications to Educational Testing , 1998 .

[23]  K. Lange An adaptive barrier method for convex programming , 1994 .

[24]  Peter G. M. van der Heijden,et al.  The EM algorithm for latent class analysis with equality constraints , 1992 .

[25]  K. Lange A gradient algorithm locally equivalent to the EM algorithm , 1995 .

[26]  Sik-Yum Lee,et al.  Covariance structure analysis in several populations , 1982 .

[27]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[28]  Gilberto A. Paula,et al.  Restricted methods in symmetrical linear regression models , 2005, Comput. Stat. Data Anal..

[29]  R. Darrell Bock,et al.  Fitting a response model forn dichotomously scored items , 1970 .

[30]  David Rindskopf,et al.  Parameterizing inequality constraints on unique variances in linear structural models , 1983 .

[31]  Kenneth Lange,et al.  Numerical analysis for statisticians , 1999 .

[32]  Peter M. Bentler,et al.  Covariance Structures Under Polynomial Constraints: Applications to Correlation and Alpha-Type Structural Models , 1983 .

[33]  K. G. J8reskoC,et al.  Simultaneous Factor Analysis in Several Populations , 2007 .