共查询到20条相似文献,搜索用时 31 毫秒
1.
Silvia Cagnone Dr Irini Moustaki Vassilis Vasdekis 《The British journal of mathematical and statistical psychology》2009,62(2):401-415
The paper proposes a full information maximum likelihood estimation method for modelling multivariate longitudinal ordinal variables. Two latent variable models are proposed that account for dependencies among items within time and between time. One model fits item‐specific random effects which account for the between time points correlations and the second model uses a common factor. The relationships between the time‐dependent latent variables are modelled with a non‐stationary autoregressive model. The proposed models are fitted to a real data set. 相似文献
2.
Regression among factor scores 总被引:1,自引:0,他引:1
Structural equation models with latent variables are sometimes estimated using an intuitive three-step approach, here denoted
factor score regression. Consider a structural equation model composed of an explanatory latent variable and a response latent
variable related by a structural parameter of scientific interest. In this simple example estimation of the structural parameter
proceeds as follows: First, common factor models areseparately estimated for each latent variable. Second, factor scores areseparately assigned to each latent variable, based on the estimates. Third, ordinary linear regression analysis is performed among the
factor scores producing an estimate for the structural parameter. We investigate the asymptotic and finite sample performance
of different factor score regression methods for structural equation models with latent variables. It is demonstrated that
the conventional approach to factor score regression performs very badly. Revised factor score regression, using Regression
factor scores for the explanatory latent variables and Bartlett scores for the response latent variables, produces consistent
estimators for all parameters. 相似文献
3.
Peter van Rijn Frank Rijmen 《The British journal of mathematical and statistical psychology》2015,68(1):1-22
Many probabilistic models for psychological and educational measurements contain latent variables. Well‐known examples are factor analysis, item response theory, and latent class model families. We discuss what is referred to as the ‘explaining‐away’ phenomenon in the context of such latent variable models. This phenomenon can occur when multiple latent variables are related to the same observed variable, and can elicit seemingly counterintuitive conditional dependencies between latent variables given observed variables. We illustrate the implications of explaining away for a number of well‐known latent variable models by using both theoretical and real data examples. 相似文献
4.
Different latent variable models have been used to analyze ordinal categorical data which can be conceptualized as manifestations of an unobserved continuous variable. In this paper, we propose a unified framework based on a general latent variable model for the comparison of treatments with ordinal responses. The latent variable model is built upon the location-scale family and is rich enough to include many important existing models for analyzing ordinal categorical variables, including the proportional odds model, the ordered probit-type model, and the proportional hazards model. A flexible estimation procedure is proposed for the identification and estimation of the general latent variable model, which allows for the location and scale parameters to be freely estimated. The framework advances the existing methods by enabling many other popular models for analyzing continuous variables to be used to analyze ordinal categorical data, thus allowing for important statistical inferences such as location and/or dispersion comparisons among treatments to be conveniently drawn. Analysis on real data sets is used to illustrate the proposed methods. 相似文献
5.
Chun Wang Hua‐Hua Chang Jeffrey A. Douglas 《The British journal of mathematical and statistical psychology》2013,66(1):144-168
The item response times (RTs) collected from computerized testing represent an underutilized source of information about items and examinees. In addition to knowing the examinees’ responses to each item, we can investigate the amount of time examinees spend on each item. In this paper, we propose a semi‐parametric model for RTs, the linear transformation model with a latent speed covariate, which combines the flexibility of non‐parametric modelling and the brevity as well as interpretability of parametric modelling. In this new model, the RTs, after some non‐parametric monotone transformation, become a linear model with latent speed as covariate plus an error term. The distribution of the error term implicitly defines the relationship between the RT and examinees’ latent speeds; whereas the non‐parametric transformation is able to describe various shapes of RT distributions. The linear transformation model represents a rich family of models that includes the Cox proportional hazards model, the Box–Cox normal model, and many other models as special cases. This new model is embedded in a hierarchical framework so that both RTs and responses are modelled simultaneously. A two‐stage estimation method is proposed. In the first stage, the Markov chain Monte Carlo method is employed to estimate the parametric part of the model. In the second stage, an estimating equation method with a recursive algorithm is adopted to estimate the non‐parametric transformation. Applicability of the new model is demonstrated with a simulation study and a real data application. Finally, methods to evaluate the model fit are suggested. 相似文献
6.
《The British journal of mathematical and statistical psychology》2003,56(2):337-357
Previous work on a general class of multidimensional latent variable models for analysing ordinal manifest variables is extended here to allow for direct covariate effects on the manifest ordinal variables and covariate effects on the latent variables. A full maximum likelihood estimation method is used to estimate all the model parameters simultaneously. Goodness‐of‐fit statistics and standard errors are discussed. Two examples from the 1996 British Social Attitudes Survey are used to illustrate the methodology. 相似文献
7.
Cécile Proust‐Lima Hélène Amieva Hélène Jacqmin‐Gadda 《The British journal of mathematical and statistical psychology》2013,66(3):470-487
Multivariate ordinal and quantitative longitudinal data measuring the same latent construct are frequently collected in psychology. We propose an approach to describe change over time of the latent process underlying multiple longitudinal outcomes of different types (binary, ordinal, quantitative). By relying on random‐effect models, this approach handles individually varying and outcome‐specific measurement times. A linear mixed model describes the latent process trajectory while equations of observation combine outcome‐specific threshold models for binary or ordinal outcomes and models based on flexible parameterized non‐linear families of transformations for Gaussian and non‐Gaussian quantitative outcomes. As models assuming continuous distributions may be also used with discrete outcomes, we propose likelihood and information criteria for discrete data to compare the goodness of fit of models assuming either a continuous or a discrete distribution for discrete data. Two analyses of the repeated measures of the Mini‐Mental State Examination, a 20‐item psychometric test, illustrate the method. First, we highlight the usefulness of parameterized non‐linear transformations by comparing different flexible families of transformation for modelling the test as a sum score. Then, change over time of the latent construct underlying directly the 20 items is described using two‐parameter longitudinal item response models that are specific cases of the approach. 相似文献
8.
9.
Karl Schweizer 《Multivariate behavioral research》2013,48(6):938-955
The standardization of loadings gives a metric to the corresponding latent variable and thus scales the variance of this latent variable. By assigning an appropriately estimated weight to all the loadings on the same latent variable it can be achieved that the average squared loading is 1 as the result of standardization. As a consequence, there is comparability of the variances of the latent variables of a confirmatory factor model. A precondition of comparability is that the latent variables must have loadings of the same manifest variables and that the variances are estimated with respect to the same covariance matrix. The usefulness of this standardization method is demonstrated by applying it for the evaluation of the sources of performance in a working memory task and for the evaluation of the impact of the position effect on performance in completing a reasoning measure. In these examples the scaled variances of the latent variables provided useful information. 相似文献
10.
This paper proposes a structural analysis for generalized linear models when some explanatory variables are measured with
error and the measurement error variance is a function of the true variables. The focus is on latent variables investigated
on the basis of questionnaires and estimated using item response theory models. Latent variable estimates are then treated
as observed measures of the true variables. This leads to a two-stage estimation procedure which constitutes an alternative
to a joint model for the outcome variable and the responses given to the questionnaire. Simulation studies explore the effect
of ignoring the true error structure and the performance of the proposed method. Two illustrative examples concern achievement
data of university students. Particular attention is given to the Rasch model. 相似文献
11.
Composite links and exploded likelihoods are powerful yet simple tools for specifying a wide range of latent variable models.
Applications considered include survival or duration models, models for rankings, small area estimation with census information,
models for ordinal responses, item response models with guessing, randomized response models, unfolding models, latent class
models with random effects, multilevel latent class models, models with log-normal latent variables, and zero-inflated Poisson
models with random effects. Some of the ideas are illustrated by estimating an unfolding model for attitudes to female work
participation.
We wish to thank The Research Council of Norway for a grant supporting our collaboration. 相似文献
12.
A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a response model and a structural model for the latent variables. The response model generalizes GLMMs to incorporate factor structures in addition to random intercepts and coefficients. As in GLMMs, the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lower-level units in the higher-level units and missing data. A wide range of response processes can be modeled including ordered and unordered categorical responses, counts, and responses of mixed types. The structural model is similar to the structural part of a SEM except that it may include latent and observed variables varying at different levels. For example, unit-level latent variables (factors or random coefficients) can be regressed on cluster-level latent variables. Special cases of this framework are explored and data from the British Social Attitudes Survey are used for illustration. Maximum likelihood estimation and empirical Bayes latent score prediction within the GLLAMM framework can be performed using adaptive quadrature in gllamm, a freely available program running in Stata.gllamm can be downloaded from http://www.gllamm.org. The paper was written while Sophia Rabe-Hesketh was employed at and Anders Skrondal was visiting the Department of Biostatistics and Computing, Institute of Psychiatry, King's College London. 相似文献
13.
Professor Sik‐Yum Lee Xin‐Yuan Song Jing‐Heng Cai Wing‐Yee So Ching‐Wang Ma Chung‐Ngor Juliana Chan 《The British journal of mathematical and statistical psychology》2009,62(2):327-347
Structural equation models (SEMs) have been widely applied to examine interrelationships among latent and observed variables in social and psychological research. Motivated by the fact that correlated discrete variables are frequently encountered in practical applications, a non‐linear SEM that accommodates covariates, and mixed continuous, ordered, and unordered categorical variables is proposed. Maximum likelihood methods for estimation and model comparison are discussed. One real‐life data set about cardiovascular disease is used to illustrate the methodologies. 相似文献
14.
Prince P. Osei Philip T. Reiss 《The British journal of mathematical and statistical psychology》2023,76(1):1-19
In many psychological studies, in particular those conducted by experience sampling, mental states are measured repeatedly for each participant. Such a design allows for regression models that separate between- from within-person, or trait-like from state-like, components of association between two variables. But these models are typically designed for continuous variables, whereas mental state variables are most often measured on an ordinal scale. In this paper we develop a model for disaggregating between- from within-person effects of one ordinal variable on another. As in standard ordinal regression, our model posits a continuous latent response whose value determines the observed response. We allow the latent response to depend nonlinearly on the trait and state variables, but impose a novel penalty that shrinks the fit towards a linear model on the latent scale. A simulation study shows that this penalization approach is effective at finding a middle ground between an overly restrictive linear model and an overfitted nonlinear model. The proposed method is illustrated with an application to data from the experience sampling study of Baumeister et al. (2020, Personality and Social Psychology Bulletin, 46, 1631). 相似文献
15.
Jing‐Heng Cai Xin‐Yuan Song 《The British journal of mathematical and statistical psychology》2010,63(3):491-508
Structural equation models (SEMs) have become widely used to determine the interrelationships between latent and observed variables in social, psychological, and behavioural sciences. As heterogeneous data are very common in practical research in these fields, the analysis of mixture models has received a lot of attention in the literature. An important issue in the analysis of mixture SEMs is the presence of missing data, in particular of data missing with a non‐ignorable mechanism. However, only a limited amount of work has been done in analysing mixture SEMs with non‐ignorable missing data. The main objective of this paper is to develop a Bayesian approach for analysing mixture SEMs with an unknown number of components and non‐ignorable missing data. A simulation study shows that Bayesian estimates obtained by the proposed Markov chain Monte Carlo methods are accurate and the Bayes factor computed via a path sampling procedure is useful for identifying the correct number of components, selecting an appropriate missingness mechanism, and investigating various effects of latent variables in the mixture SEMs. A real data set on a study of job satisfaction is used to demonstrate the methodology. 相似文献
16.
Two Studies Examining the Error Theory Underlying the Measurement Model of the Verbal Aggressiveness Scale
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Meta‐analysis indicates moderate correlations between the Verbal Aggressiveness Scale (VAS) and other self‐report measures but near‐zero correlations with behavioral measures. Accurately interpreting correlations between the VAS and other variables, however, requires an examination of the untested error theory underlying the measurement model for the VAS. In two separate studies, the results of single‐factor correlated uniqueness confirmatory factor analytic models revealed a pattern of significant error covariances indicating that VAS item scores are confounded by systematic error attributable to multiple unspecified latent effects. After pruning the item sets, we identified 4 items that were free of latent variable influences other than trait verbal aggressiveness. Implications for interpreting the verbal aggressiveness literature are discussed along with recommendations for revising the VAS. 相似文献
17.
The paper proposes a composite likelihood estimation approach that uses bivariate instead of multivariate marginal probabilities for ordinal longitudinal responses using a latent variable model. The model considers time-dependent latent variables and item-specific random effects to be accountable for the interdependencies of the multivariate ordinal items. Time-dependent latent variables are linked with an autoregressive model. Simulation results have shown composite likelihood estimators to have a small amount of bias and mean square error and as such they are feasible alternatives to full maximum likelihood. Model selection criteria developed for composite likelihood estimation are used in the applications. Furthermore, lower-order residuals are used as measures-of-fit for the selected models. 相似文献
18.
In this paper we introduce a latent variable model (LVM) for mixed ordinal and continuous responses, where covariate effects
on the continuous latent variables are modelled through a flexible semiparametric Gaussian regression model. We extend existing
LVMs with the usual linear covariate effects by including nonparametric components for nonlinear effects of continuous covariates
and interactions with other covariates as well as spatial effects. Full Bayesian modelling is based on penalized spline and
Markov random field priors and is performed by computationally efficient Markov chain Monte Carlo (MCMC) methods. We apply
our approach to a German social science survey which motivated our methodological development.
We thank the editor and the referees for their constructive and helpful comments, leading to substantial improvements of a
first version, and Sven Steinert for computational assistance. Partial financial support from the SFB 386 “Statistical Analysis
of Discrete Structures” is also acknowledged. 相似文献
19.
The common factor model assumes that the linear coefficients (intercepts and factor loadings) linking the observed variables to the latent factors are fixed coefficients (i.e., common for all participants). When the observed variables are participants' observed responses to stimuli, such as their responses to the items of a questionnaire, the assumption of common linear coefficients may be too restrictive. For instance, this may occur if participants consistently use the response scale idiosyncratically. To account for this phenomenon, the authors partially relax the fixed coefficients assumption by allowing the intercepts in the factor model to change across participants. The model is attractive when m factors are expected on the basis of substantive theory but m + 1 factors are needed in practice to adequately reproduce the data. Also, this model for single-level data can be fitted with conventional software for structural equation modeling. The authors demonstrate the use of this model with an empirical data set on optimism in which they compare it with competing models such as the bifactor and the correlated trait-correlated method minus 1 models. 相似文献
20.
Matthias von Davier 《The British journal of mathematical and statistical psychology》2014,67(1):49-71
The ‘deterministic‐input noisy‐AND’ (DINA) model is one of the more frequently applied diagnostic classification models for binary observed responses and binary latent variables. The purpose of this paper is to show that the model is equivalent to a special case of a more general compensatory family of diagnostic models. Two equivalencies are presented. Both project the original DINA skill space and design Q ‐matrix using mappings into a transformed skill space as well as a transformed Q ‐matrix space. Both variants of the equivalency produce a compensatory model that is mathematically equivalent to the (conjunctive) DINA model. This equivalency holds for all DINA models with any type of Q ‐matrix, not only for trivial (simple‐structure) cases. The two versions of the equivalency presented in this paper are not implied by the recently suggested log‐linear cognitive diagnosis model or the generalized DINA approach. The equivalencies presented here exist independent of these recently derived models since they solely require a linear – compensatory – general diagnostic model without any skill interaction terms. Whenever it can be shown that one model can be viewed as a special case of another more general one, conclusions derived from any particular model‐based estimates are drawn into question. It is widely known that multidimensional models can often be specified in multiple ways while the model‐based probabilities of observed variables stay the same. This paper goes beyond this type of equivalency by showing that a conjunctive diagnostic classification model can be expressed as a constrained special case of a general compensatory diagnostic modelling framework. 相似文献