A nonlinear mixed model framework for item response theory.

Mixed models take the dependency between observations based on the same cluster into account by introducing 1 or more random effects. Common item response theory (IRT) models introduce latent person variables to model the dependence between responses of the same participant. Assuming a distribution for the latent variables, these IRT models are formally equivalent with nonlinear mixed models. It is shown how a variety of IRT models can be formulated as particular instances of nonlinear mixed models. The unifying framework offers the advantage that relations between different IRT models become explicit and that it is rather straightforward to see how existing IRT models can be adapted and extended. The approach is illustrated with a self-report study on anger. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Ramsay-curve item response theory (RC-IRT) to detect and correct for nonnormal latent variables.

Popular methods for fitting unidimensional item response theory (IRT) models to data assume that the latent variable is normally distributed in the population of respondents, but this can be unreasonable for some variables. Ramsay-curve IRT (RC-IRT) was developed to detect and correct for this nonnormality. The primary aims of this article are to introduce RC-IRT less technically than it has been described elsewhere; to evaluate RC-IRT for ordinal data via simulation, including new approaches for model selection; and to illustrate RC-IRT with empirical examples. The empirical examples demonstrate the utility of RC-IRT for real data, and the simulation study indicates that when the latent distribution is skewed, RC-IRT results can be more accurate than those based on the normal model. Along with a plot of candidate curves, the Hannan-Quinn criterion is recommended for model selection. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Estimating, testing, and comparing specific effects in structural equation models: The phantom model approach.

The phantom model approach for estimating, testing, and comparing specific effects within structural equation models (SEMs) is presented. The rationale underlying this novel method consists in representing the specific effect to be assessed as a total effect within a separate latent variable model, the phantom model that is added to the main model. The following favorable features characterize the method: (a) It enables the estimation, testing, and comparison of arbitrary specific effects for recursive and nonrecursive models with latent and manifest variables; (b) it enables the bootstrapping of confidence intervals; and (c) it can be applied with all standard SEM programs permitting latent variables, the specification of equality constraints, and the bootstrapping of total effects. These features along with the fact that no manipulation of matrices and formulas is required make the approach particularly suitable for applied researchers. The method is illustrated by means of 3 examples with real data sets. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

The use of causal indicators in covariance structure models: Some practical issues.

In conventional representations of covariance structure models, indicators are defined as linear functions of latent variables, plus error. In an alternative representation, constructs can be defined as linear functions of their indicators, called causal indicators, plus an error term. Such constructs are not latent variables but composite variables, and they have no indicators in the conventional sense. The presence of composite variables in a model can, in some situations, result in problems with identification of model parameters. Also, the use of causal indicators can produce models that imply zero correlation among many measured variables, a problem resolved only by the inclusion of a potentially large number of additional parameters. These phenomena are demonstrated with an example, and general principles underlying them are discussed. Remedies are described so as to allow for the evaluation of models that contain causal indicators. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Variational learning in nonlinear gaussian belief networks

We view perceptual tasks such as vision and speech recognition as inference problems where the goal is to estimate the posterior distribution over latent variables (e.g., depth in stereo vision) given the sensory input. The recent flurry of research in independent component analysis exemplifies the importance of inferring the continuous-valued latent variables of input data. The latent variables found by this method are linearly related to the input, but perception requires nonlinear inferences such as classification and depth estimation. In this article, we present a unifying framework for stochastic neural networks with nonlinear latent variables. Nonlinear units are obtained by passing the outputs of linear gaussian units through various nonlinearities. We present a general variational method that maximizes a lower bound on the likelihood of a training set and give results on two visual feature extraction problems. We also show how the variational method can be used for pattern classification and compare the performance of these nonlinear networks with other methods on the problem of handwritten digit recognition.     

A tetrad test for causal indicators.

The authors propose a confirmatory tetrad analysis test to distinguish causal from effect indicators in structural equation models. The test uses "nested" vanishing tetrads that are often implied when comparing causal and effect indicator models. The authors present typical models that researchers can use to determine the vanishing tetrads for 4 or more variables. They also provide the vanishing tetrads for mixtures of causal and effect indicators, for models with fewer than 4 indicators per latent variable, or for cases with correlated errors. The authors illustrate the test results for several simulation and empirical examples and emphasize that their technique is a theory-testing rather than a model-generating approach. They also review limitations of the procedure including the indistinguishable tetrad equivalent models, the largely unknown finite sample behavior of the test statistic, and the inability of any procedure to fully validate a model specification. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Psychometric approaches for developing commensurate measures across independent studies: Traditional and new models.

[Correction Notice: An erratum for this article was reported in Vol 14(4) of Psychological Methods (see record 2009-22665-007). In this article, the authors wrote, "To our knowledge, the multisample framework is the only available option within these [latent variable] programs that allows for the moderation of all types of parameters, and this approach requires a single categorical moderator variable to define the samples.” Bengt Muthén has clarified for the authors that some programs, including Mplus and Mx, can allow for continuous moderation through the implementation of nonlinear constraints involving observed variables, further enlarging the class of MNLFA models that can be fit with these programs.] When conducting an integrative analysis of data obtained from multiple independent studies, a fundamental problem is to establish commensurate measures for the constructs of interest. Fortunately, procedures for evaluating and establishing measurement equivalence across samples are well developed for the linear factor model and commonly used item response theory models. A newly proposed moderated nonlinear factor analysis model generalizes these models and procedures, allowing for items of different scale types (continuous or discrete) and differential item functioning across levels of categorical and/or continuous variables. The potential of this new model to resolve the problem of measurement in integrative data analysis is shown via an empirical example examining changes in alcohol involvement from ages 10 to 22 years across 2 longitudinal studies. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Latent variable interaction and quadratic effect estimation: A two-step technique using structural equation analysis.

The author proposes an alternative estimation technique for latent variable interactions and quadratics. Available techniques for specifying these variables in structural equation models require adding variables or constraint equations that can produce specification tedium and errors or estimation difficulties. The proposed technique avoids these difficulties and may be useful for EQS, LISREL 7, and LISREL 8 users. First, measurement parameters for indicator loadings and errors of linear latent variables are estimated in a measurement model that excludes the interaction and quadratic variables. Next, these estimates are used to calculate values for the indicator loadings and error variances of the interaction and quadratic latent variables. Then, these calculated values are specified as constants in the structural model containing the interaction and quadratic variables. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The Integration of Continuous and Discrete Latent Variable Models: Potential Problems and Promising Opportunities.

Structural equation mixture modeling (SEMM) integrates continuous and discrete latent variable models. Drawing on prior research on the relationships between continuous and discrete latent variable models, the authors identify 3 conditions that may lead to the estimation of spurious latent classes in SEMM: misspecification of the structural model, nonnormal continuous measures, and nonlinear relationships among observed and/or latent variables. When the objective of a SEMM analysis is the identification of latent classes, these conditions should be considered as alternative hypotheses and results should be interpreted cautiously. However, armed with greater knowledge about the estimation of SEMMs in practice, researchers can exploit the flexibility of the model to gain a fuller understanding of the phenomenon under study. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A new method to estimate parameters of linear compartmental models using artificial neural networks

At present, the preferred tool for parameter estimation in compartmental analysis is an iterative procedure; weighted nonlinear regression. For a large number of applications, observed data can be fitted to sums of exponentials whose parameters are directly related to the rate constants/coefficients of the compartmental models. Since weighted nonlinear regression often has to be repeated for many different data sets, the process of fitting data from compartmental systems can be very time consuming. Furthermore the minimization routine often converges to a local (as opposed to global) minimum. In this paper, we examine the possibility of using artificial neural networks instead of weighted nonlinear regression in order to estimate model parameters. We train simple feed-forward neural networks to produce as outputs the parameter values of a given model when kinetic data are fed to the networks' input layer. The artificial neural networks produce unbiased estimates and are orders of magnitude faster than regression algorithms. At noise levels typical of many real applications, the neural networks are found to produce lower variance estimates than weighted nonlinear regression in the estimation of parameters from mono- and biexponential models. These results are primarily due to the inability of weighted nonlinear regression to converge. These results establish that artificial neural networks are powerful tools for estimating parameters for simple compartmental models.     

Genetic-Fuzzy Approach for Modeling Complex Systems with an Example Application in Masonry Bond Strength Prediction

A genetic-fuzzy learning from examples (GFLFE) approach is presented for determining fuzzy rule bases generated from input/output data sets. The method is less computationally intensive than existing fuzzy rule base learning algorithms as the optimization variables are limited to the membership function widths of a single rule, which is equal to the number of input variables to the fuzzy rule base. This is accomplished by primary width optimization of a fuzzy learning from examples algorithm. The approach is demonstrated by a case study in masonry bond strength prediction. This example is appropriate as theoretical models to predict masonry bond strength are not available. The GFLFE method is compared to a similar learning method using constrained nonlinear optimization. The writers’ results indicate that the use of a genetic optimization strategy as opposed to constrained nonlinear optimization provides significant improvement in the fuzzy rule base as indicated by a reduced fitness (objective) function and reduced root-mean-squared error of an evaluation data set.     

The theoretical status of latent variables.

This article examines the theoretical status of latent variables as used in modern test theory models. First, it is argued that a consistent interpretation of such models requires a realist ontology for latent variables. Second, the relation between latent variables and their indicators is discussed. It is maintained that this relation can be interpreted as a causal one but that in measurement models for interindividual differences the relation does not apply to the level of the individual person. To substantiate intraindividual causal conclusions, one must explicitly represent individual level processes in the measurement model. Several research strategies that may be useful in this respect are discussed, and a typology of constructs is proposed on the basis of this analysis. The need to link individual processes to latent variable models for interindividual differences is emphasized. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Analysis of multivariate frequency data by graphical models and generalizations of the multidimensional row-column association model.

Models used to analyze cross-classifications of counts from psychological experiments must represent associations between multiple discrete variables and take into account attributes of stimuli, experimental conditions, or characteristics of subjects. The models must also lend themselves to psychological interpretations about underlying structures mediating the relationship between stimuli and responses. To meet these needs, the author extends the graphical latent variable models for nominal and/or ordinal data proposed by C. J. Anderson and J. K. Vermunt (2000) to situations in which dependencies between observed variables are not fully accounted for by the latent variables. The graphical models provide a unified framework for studying multivariate associations that include log-linear models and log-multiplicative association models as special cases. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

"Psychometric approaches for developing commensurate measures across independent studies: Traditional and new models": Clarification to Bauer and Hussong (2009).

Reports a clarification to "Psychometric approaches for developing commensurate measures across independent studies: Traditional and new models" by Daniel J. Bauer and Andrea M. Hussong (Psychological Methods, 2009[Jun], Vol 14[2], 101-125). In this article, the authors wrote, "To our knowledge, the multisample framework is the only available option within these [latent variable] programs that allows for the moderation of all types of parameters, and this approach requires a single categorical moderator variable to define the samples.” Bengt Muthén has clarified for the authors that some programs, including Mplus and Mx, can allow for continuous moderation through the implementation of nonlinear constraints involving observed variables, further enlarging the class of MNLFA models that can be fit with these programs. (The following abstract of the original article appeared in record 2009-08072-001.) When conducting an integrative analysis of data obtained from multiple independent studies, a fundamental problem is to establish commensurate measures for the constructs of interest. Fortunately, procedures for evaluating and establishing measurement equivalence across samples are well developed for the linear factor model and commonly used item response theory models. A newly proposed moderated nonlinear factor analysis model generalizes these models and procedures, allowing for items of different scale types (continuous or discrete) and differential item functioning across levels of categorical and/or continuous variables. The potential of this new model to resolve the problem of measurement in integrative data analysis is shown via an empirical example examining changes in alcohol involvement from ages 10 to 22 years across 2 longitudinal studies. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Structural-equation models of current drug use: Are appropriate models so simple(x)?

The simplex and common-factor models of drug use were compared using maximum-likelihood estimation of latent variable structural models in two samples: a sample of 226 high school students, using ratio-scale measures of current drug use, and a sample of 310 industrial workers and 811 college students, using ordinal-scale measures of current drug use. Latent variables of alcohol, marihuana, enhancer hard drugs, and dampener hard drugs were specified in a series of structural models. Contrary to previous findings with cumulative drug-use data, the common-factor model provided a more acceptable representation of the observed current-use data than did the simplex model in both samples. In addition, the similarity of results across both of these samples supports recent contentions by Huba and Bentler (1982) that quantitatively measured variables are not necessarily superior to qualitative, ordinal indicators in latent variable models of drug use. (49 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Consistent Finite-Element Response Sensitivity Analysis

This paper examines the important issue of response sensitivities of dynamic models of structural systems to both material and (discrete) loading parameters. Plasticity-based finite-element models of structural systems subjected to base excitation such as earthquake loading are considered. The two methods for computing the response sensitivities, namely, (1) discretizing in time the time continuous-spatially discrete response equations and differentiating the resulting time discrete-spatially discrete response equations with respect to sensitivity parameters, and (2) differentiating the time continuous-spatially discrete response equations with respect to sensitivity parameters and discretizing in time the resulting time continuous-spatially discrete response sensitivity equations, are clearly distinguished. The discontinuities in time of the response sensitivities arising due to material state transitions in the plasticity models, and their propagation from the quadrature point level to the global structural response level are discussed using a specific one-dimensional plasticity model. The procedure to obtain the exact sensitivities of the numerical nonlinear finite-element response, including proper capture of their discontinuities, is formalized. Application examples illustrating the concepts are presented at the end.     

A double-structure structural equation model for three-mode data.

Structural equation models are commonly used to analyze 2-mode data sets, in which a set of objects is measured on a set of variables. The underlying structure within the object mode is evaluated using latent variables, which are measured by indicators coming from the variable mode. Additionally, when the objects are measured under different conditions, 3-mode data arise, and with this, the simultaneous study of the correlational structure of 2 modes may be of interest. In this article the authors present a model with a simultaneous latent structure for 2 of the 3 modes of such a data set. They present an empirical illustration of the method using a 3-mode data set (person by situation by response) exploring the structure of anger and irritation across different interpersonal situations as well as across persons. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Random effects models in latent class analysis for evaluating accuracy of diagnostic tests

When the results of a reference (or gold standard) test are missing or not error-free, the accuracy of diagnostic tests is often assessed through latent class models with two latent classes, representing diseased or nondiseased status. Such models, however, require that conditional on the true disease status, the tests are statistically independent, an assumption often violated in practice. Consequently, the model generally fits the data poorly. In this paper, we develop a general latent class model with random effects to model the conditional dependence among multiple diagnostic tests (or readers). We also develop a graphical method for checking whether or not the conditional dependence is of concern and for identifying the pattern of the correlation. Using the random-effects model and the graphical method, a simple adequate model that is easy to interpret can be obtained. The methods are illustrated with three examples from the biometric literature. The proposed methodology is also applicable when the true disease status is indeed known and conditional dependence could well be present.