Showing papers on "Latent variable model published in 1990"

Latent curve analysis

Abstract: As a method for representing development, latent trait theory is presented in terms of a statistical model containing individual parameters and a structure on both the first and second moments of the random variables reflecting growth. Maximum likelihood parameter estimates and associated asymptotic tests follow directly. These procedures may be viewed as an alternative to standard repeated measures ANOVA and to first-order auto-regressive methods. As formulated, the model encompasses cohort sequential designs and allow for period or practice effects. A numerical illustration using data initially collected by Nesselroade and Baltes is presented.

Rasch models in latent classes: An integration of two approaches to item analysis

Abstract: A model is proposed that combines the theoret ical strength of the Rasch model with the heuristic power of latent class analysis. It assumes that the Rasch model holds for all persons within a latent class, but it allows for different sets of item parameters between the latent classes. An estima tion algorithm is outlined that gives conditional maximum likelihood estimates of item parameters for each class. No a priori assumption about the item order in the latent classes or the class sizes is required. Application of the model is illustrated, both for simulated data and for real data.

A New Item Response Theory Modeling Approach with Applications to Unidimensionality Assessment and Ability Estimation

Abstract: Using an infinite item test framework, it is argued that the usual assumption of local independence be replaced by a weaker assumption,essential independence. A fortiori, the usual assumption of unidimensionality is replaced by a weaker and arguably more appropriatestatistically testable assumption of essential unidimennsionality. Essential unidimennsionnality implies the existence of a “unique” unidimensional latent ability. Essential unidimensionality is equivalent to the “consistent” estimation of this latnet ability in an ordinal scaling sense using anyBalanced empirical scaling. A variation of this estimation approach allows consistent estimation of ability on the given latent ability scale.

Problems in the measurement of latent variables in structural equations causal models

Abstract: Some problems in the measurement of latent variables in structural equations causal models are presented, with examples from recent empirical studies. Latent variables that are theoretically the source of correlation among the empirical indica tors are differentiated from unmeasured variables that are related to the empirical indicators for other reasons. It is pointed out that these should also be represented by different analytical models, and that much published research has treated this distinction as if it had no analytic consequences. The connection between this theoretical distinction and disattenuation effects in latent variable models is shown, and problems with these estimates are discussed. Finally, recommendations are made for decisions about whether and how to measure latent variables when manifest variables are potentially available.

Sequential item response models with an ordered response

Abstract: A stepwise approach to the construction of latent trait models is outlined. As a special case of the derived general sequential model, a sequential Rasch model is considered. The derivation of the models is based on mechanisms of latent random variables. The unconditional maximum likelihood estimation is embedded in the framework of generalized linear models. An alternative estimation procedure which allows for ‘parameter separability’ is considered and its applicability is shown.

The Robustness of Estimates of Total Indirect Effects in Covariance Structure Models Estimated by Maximum Likelihood.

Abstract: The large sample distribution of total indirect effects in covariance structure models in well known. Using Monte Carlo methods, this study examines the applicability of the large sample theory to maximum likelihood estimates oftotal indirect effects in sample sizes of 50, 100, 200, 400, and 800. Two models are studied. Model 1 is a recursive model with observable variables and Model 2 is a nonrecursive model with latent variables. For the large sample theory to apply, the results suggest that sample szes of 200 or more and 400 or more are required for models such as Model 1 and Model 2, respectively.

Latent class analysis with ordered latent classe

Abstract: In this paper a latent class model is described in which the latent classes are ordered imposing inequality constraints on item response and cumulative response probabilities from subsequent latent classes. These inequality constraints are derived from the basic assumption that, when the latent classes may be ordered from low to high along the latent continuum, the probability of a ‘positive’ response should increase monotonically as one moves along this continuum. An algorithm to obtain the maximum likelihood estimates of the model parameters is proposed and is applied to a real data set.

The Use of Loglinear Models for Assessing Differential Item Functioning Across Manifest and Latent Examinee Groups

Abstract: Loglinear latent class models are used to detect differential item functioning (DIF). These models are formulated in such a manner that the attribute to be assessed may be continuous, as in a Rasch model, or categorical, as in Latent Class Mastery models. Further, an item may exhibit DIF with respect to a manifest grouping variable, a latent grouping variable, or both. Likelihood-ratio tests for assessing the presence of various types of DIF are described, and these methods are illustrated through the analysis of a "real world" data set.

The Dutch Identity: A New Tool for the Study of Item Response Models.

Abstract: The Dutch Identity is a useful way to reexpress the basic equations of item response models that relate the manifest probabilities to the item response functions (IRFs) and the latent trait distribution. The identity may be exploited in several ways. For example: (a) to suggest how item response models behave for large numbers of items—they are approximate submodels of second-order loglinear models for 2 J tables; (b) to suggest new ways to assess the dimensionality of the latent trait—principle components analysis of matrices composed of second-order interactions from loglinear models; (c) to give insight into the structure of latent class models; and (d) to illuminate the problem of identifying the IRFs and the latent trait distribution from sample data.

A latent trait model for dichotomous choice data

Abstract: The PARELLA model is a probabilistic parallelogram model that can be used for the measurement of latent attitudes or latent preferences. The data analyzed are the dichotomous responses of persons to stimuli, with a one (zero) indicating agreement (disagreement) with the content of the stimulus. The model provides a unidimensional representation of persons and items. The response probabilities are a function of the distance between person and stimulus: the smaller the distance, the larger the probability that a person will agree with the content of the stimulus. An estimation procedure based on expectation maximization and marginal maximum likelihood is developed and the quality of the resulting parameter estimates evaluated.

Continuous and discrete latent structure models for item response data

Abstract: Relations are examined between latent trait and latent class models for item response data. Conditions are given for the two-latent class and two-parameter normal ogive models to agree, and relations between their item parameters are presented. Generalizationss are then made to continuous models with more than one latent trait and discrete models with more than two latent classes, and methods are presented for relating latent class models to factor models for dichotomized variables. Results are illustrated using data from the Law School Admission Test, previously analyzed by several authors.

Parametric statistics and levels of measurement : factorial designs and multiple regression

Abstract: Let Y be a continuous, ordinal measure of a latent variable θ. In general, for factorial designs, an analysis of variance of the observed variable Y cannot be used to draw inferences about main effects and interactions on the latent variable θ even when the standard normality and equality of variance assumptions hold.

A latent time–budget model

Abstract: Time–budgets summarize how the time of objects is distributed over a number of categories. Usually they are collected in object by category matrices with the property that rows of this data matrix add up to one. In this paper we discuss a model for the analysis of time–budgets that used this property. The model approximates the observed time–budgets by weighted sums of a number of latent time–budgets. These latent time–budgets determine the behavior of all objects. Special attention is given to the identification of the model. The model is compared with logcontrast principal component analysis.

Least Squares and Latent Variables.

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Searching for parsimony: are true-score models or factor models more appropriate?

Abstract: In this paper we have investigated two stategies for the analysis of perceptions, orientations and other mental states variables in structural equation models. The first strategy can be characterized as empiristic and inductivistic since it starts from the solid ground of observation. In a first step true scores are generated by clearing the observed scores from random measurement error. Higher-order latent variables are only introduced in a second step after passing some rigorous statistical tests. A proponent of this strategy will always emphasize that common factors and other latent constructs are rather meaningless if they are not firmly anchored at the observational level. He will therefore set up some hard criteria for common-factor models which are rarely met. As a consequence, this strategy frequently will result in pure true-score models. A proponent of the second, more deductive strategy will object that true scores do not represent the theoretical concepts he is interested in. Theory building requires some highly abstract and general concepts which can be applied to a large variety of situations. These concepts cannot be measured adequately by a single item or a single mode of behavior. In particular, if one attempts to measure a general disposition or trait, an individual's reactions should be observed at different occasions and times. Since the multiple indicator approach by and large meets this requirement, a follower of the second strategy will first try to find some parallel, tauequivalent or congeneric measures for the underlying varibles. If a simple multiple indicator model for an attitude or some other kind of orientation proves incompatible with the data, he will usually not discard the common-factor model as a whole but successively replace a simple structure by a more complicated one, for example, by freeing some additional factor loadings or by admitting systematic measurement error. Thus, the deductive approach will sometimes lead to common-factor models with a rather complex measurement structure. It is true, all of these operations aimed at the improvement of fit are not deductive at all. However, since the second strategy always aims at the adequate measurement of some theoretical concepts, it seems to be at least more deductive than the first. Both strategies have there merits and disadvantages. As can be seen from the empirical analysis of Saris and Putte, the inductivist will analyze the observed items with great care and will usually arrive at a beautifully fitting model. We have benefitted from these virtues: By adopting some of Saris and Putte's assumptions we were able to remove some implausible results from our original model. However, we were not willing to adopt the major drawbacks of the pure true-score models as well. In our view, it has led to a large amount of rather unstable oponions which, at least at present cannot be integrated in any existing theory on opinions and opinion formation. Furthermore, as we have shown in the third section, the pure true-score model becomes very complicated as soon as potential causes and consequences of the opinions are included in the structural equation model. Finally, even within the pure true-score model, Saris and Putte's assumption that the error variance remains constant across all three panel waves remains debatable. Even within the best-fitting pure true-score model the decrease of measurement error beteeen the first and second interview is significant at the 10% level. It would have been highly significant in a reexamination of the model preferred by Saris and Putte for substantive reasons. We can reject Saris and Putte's conceptualization for substantive and methodological but not empirical reasons. This is partly due to the low power of all statistical tests which in turn is due to the small sample size. Thus, our debate should be continued with better data. At present, we can only point to the major advantages of our model in which attitudes are represented by common factors. Attitudes are key concepts in many theories. They are assumed to be highly abstract and general and to indirectly influence behavior under various conditions. We have also shown that the exogenous variables age and education have a direct impact on the general attitude and not on true scores or specific factors. At least with respect to these variables, the common-factor model has proved to be much more parsimonious than the pure true-score model. There may be some other variables with a direct effect on the specific factors and not on the general attitude. However, they are usually of less theoretical interest. In our view, an additional advantage pf our conceptualization lies in the fact that some important implications of the Socratic effect can be observed in our model: In the first interview, we do not only estimate a larger amount of measurement error, but responses also seem to be distorted in the direction of social desirability. Since all these findings fit neatly with some results of psychological experiments, we will stubbornly retain the basic feature of our original conceptualization until it will be disconfirmed with better data.

Latent Class Analysis of Deluded Patients

Abstract: The internal and external construct validity of 4 severe prognostic psychopathological items is studied in deluded patients. A two-class model of latent structure analysis fits fairly well. One latent class seems to reflect a schizophrenic spectrum while the other class does not include characteristics which are known from one single nosologic entity. Thought disorder is most predictive for schizophrenic class membership, while blunted affect has the least predictive value. This 'schizophrenic' latent class has a fairly high and similar sensitivity to various definitions of schizophrenic disorder. The frequency of the types of delusions differs between the classes.

Analyzing sequential categorical data: Individual variation in markov chains

Abstract: Markov chains are probabilistic models for sequences of categorical events, with applications throughout scientific psychology. This paper provides a method for anlayzing data consisting of event sequences and covariate observations. It is assumed that each sequence is a Markov process characterized by a distinct transition probability matrix. The objective is to use the covariate data to explain differences between individuals in the transition probability matrices characterizing their sequential data. The elements of the transition probability matrices are written as functions of a vector of latent variables, with variation in the latent variables explained through a multivariate regression on the covariates. The regression is estimated using the EM algorithm, and requires the numerical calculation of a multivariate integral. An example using simulated cognitive developmental data is presented, which shows that the estimation of individual variation in the parameters of a probability model may have substantial theoretical importance, even when individual differences are not the focus of the investigator's concerns.

The Measurement of Dynamic Latent Variables in Longitudinal Aging Research: Quantifying Adult Development

Abstract: Dynamic latent variables involve systematic intraindividual change over time. Although it seems natural to apply traditional measurement theory to dynamic latent variables, in fact this is often inappropriate. Traditional measurement theory is based on the idea of static latent variables and offers little guidance to the researcher who wishes to measure a dynamic latent variable with a high degree of accuracy and validity. It is the contention of this article that measurement of a dynamic latent variable must start from a clearly defined substantive theory about human development. Two approaches that take this perspective are presented; the longitudinal Guttman simplex (LGS), a measurement model for dynamic latent variables undergoing irreversible cumulative, unitary development; and latent transition analysis (LTA), a more general latent class measurement model.

Covariance structure model when the factor means and the covariances are functions of the third variable

Abstract: A model in which factor means and factor covariances vary continuously with an external variable is discussed. We assume that, if the covariance matrix of manifest variables should have a certain structure, the means should also have a certain structure characterized by latent variables. In this paper, we discuss two kinds of models. The first is a model in which both means and a covariance matrix of latent variables are functions of an external variable. The second model has structure on the means of manifest variables, but the covariance matrix of the manifest variables is non-structured and constant across the values of the external variable

A latent-trait based reliability estimate and upper bound

Abstract: An estimate and an upper-bound estimate for the reliability of a test composed of binary items is derived from the multidimensional latent trait theory proposed by Bock and Aitkin (1981). The estimate derived here is similar to internal consistency estimates (such as coefficient alpha) in that it is a function of the correlations among test items; however, it is not a lowerbound estimate as are all other similar methods.

A latent class model for assessing learning structures

Abstract: In the present paper, we discuss a latent structure analysis for assessing learning structures of acquiring two kinds of skill. This discussion presents a “pairwise” assessment procedure for explaining the learning structure of acquiring the skills concerned. We propose a latent class model for this objective. This model explains prerequisite and transfererence relations between the skills. A parameter estimation procedure is derived by use of the EM algorithm. A numerical example is also included to illustrate the estimation procedure.