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Invited Lectures
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| Albert Maydeu-Olivares |
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Testing models for multivariate categorical data: Implications for IRT research |
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The paper reviews recent developments in the area of goodness-of-fit
testing of multivariate categorical data models. It begins by reviewing
the classical statistics: Pearson's X2 and the likelihood ratio test
statistic G2. Since the asymptotic p-values for these statistics are
inaccurate when the contingency table is sparse, we discuss
alternatives: testing solely for relative fit using the likelihood
ratio statistic, pooling cells, resampling methods, and limited
information methods.
Limited information test statistics can be derived for either full
information null hypotheses or for limited information null hypotheses.
We consider both cases.
Should an overall goodness-of-fit test indicate that the model fits
poorly it is necessary to assess the source of misfit. We discuss
testing the fit of the model in subtables. That is, tests for single
variables, pairs of variables, and triplets.
Also, it is sometimes of interest to investigate the extent to which
the model cross-validates in holdout samples. We present recent
developments in this area as well.
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| Paras Mehta |
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Measurement Invariance in IRT and Ordinal-CFA: Best of Both Worlds |
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The CFA model for discrete variables includes four parameters (thresholds, factor loadings, residual variances, and item measurement intercepts) whereas the corresponding IRT model is framed in terms of only two parameters (discrimination and difficulty parameters). Yet the two models are said to be mathematically equivalent in the single group case. The current paper explores the algebraic equivalence of the two models in the case of multiple groups. The continuous variable logic for investigating factor analytic measurement equivalence when applied to discrete variables results in several anomalous cases. These anomalies are resolved by considering the implications of the model from an IRT perspective. These insights naturally suggest a hybrid approach for evaluating measurement equivalence. The prescribed approach borrows the strengths of both approaches and circumvents the issues inherent in the factor analytic model. |
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| Sy-Miin Chow |
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Representing Dynamic Processes and Potential Nonstationarities Using Kalman Filter Techniques |
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State-space modeling techniques have been compared to structural equation
modeling techniques in various contexts but their strengths in representing
intraindividual change have not received much attention in more applied
realms. Several simulated and empirical examples will be provided to help
illustrate the potential utility of Kalman filter techniques in representing
dynamic processes and their associated non-stationarities. Emphasis is
placed on summarizing features of linear and nonlinear Kalman filter
approaches that make them particularly conducive for fitting dynamic models
with time-varying parameters. The examples considered include a harmonic
regression model in which the amplitudes associated with different cyclic
components are allowed to vary over time as autoregressive processes, a
regression model with time-varying, state-dependent parameters and a
nonlinear dynamic model whose parameters undergo more complex changes.
Implications for how state-space modeling techniques can be used to
represent affective, developmental and other related processes are
discussed. |
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| David Flora |
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Further Issues and Findings for Factor Analysis using Polychoric Correlations |
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The factor analysis of ordinal variables continues to be extremely
common in applied psychological research, particularly in studies on
the construction and validation of scales composed of Likert-type
items. Recent work has shown that limited information methods based
on polychoric correlations perform well when properly specified
models are estimated in a confirmatory (SEM) framework. However,
applied researchers often employ exploratory methods in attempts to
uncover the major factors underlying responses to Likert-type items.
Yet, although analysis of product-moment relations is inadequate for
this purpose, it remains unknown whether the polychoric correlation
approach is likely to lead to sound conclusions about the number of
major common factors and accurate parameter estimates. Simulation
results will be presented showing that the polychoric correlation
approach performs well in a variety of commonly encountered
situations, including the presence of model error (e.g., correlated
unique factors). An application will be presented that demonstrates
these issues in a practical setting. |
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| Shelley Blozis |
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On Specifying Covariance Structures in Linear Latent Curve Models to Multiple Longitudinal Variables |
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Latent curve models are increasingly used for the study of the joint
associations between the random coefficients relating to different variables
measured longitudinally. This analytic strategy is useful in estimating, for
example, the extent to which individual-level change in one variable is
related to change in another variable. In practice, it may be assumed that
two variables are related only through the linear associations between their
corresponding random effects at the second level. There are cases, however,
when the relationship between two variables extends beyond these
associations. Ignoring additional sources of dependence may have
consequences on the magnitude of the associations between the random
coefficients. This paper considers alternative covariance structures that
relax the assumption of conditional independence to yield more appropriate
values of the associations between random coefficients relating to different
variables. |
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| Jeremy Biesanz |
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Assessing differential accuracy in interpersonal judgment: Revisiting Cronbach's critiques |
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Assessing the good judge of personality and measuring individual differences in judgmental accuracy has historically presented methodological challenges. In a series of critiques of earlier research, Cronbach (e.g., Cronbach, 1955, 1958; Gage & Cronbach, 1955) presented a componential framework to help strengthen inferences of individual differences in judgmental accuracy. This approach has essentially remained unchanged since Cronbach’s critiques and assumes that impressions are measured without error. Without disentangling measurement error from impression ratings and modeling both simultaneously, many critical questions cannot be asked within Cronbach’s original framework. For example, to what extent is there meaningful variability among individuals in their social perception of personality? Does the domain matter – for instance, are there more individual differences in judgmental accuracy in perceptions of Extraversion than Conscientiousness? The present talk (a) extends Cronbach’s conceptual framework to both multilevel regression models for rating data and generalized multilevel models for paired comparison data to address such questions, (b) presents several examples to illustrate how to analyze and interpret – as well as combine – these models within Cronbach's componential framework, and (c) discusses methodological and modeling issues in assessing individual differences in judgmental accuracy. |
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Questions?
