Papers by George Macready
Applied Psychological Measurement, 2012
This study explored a computerized adaptive test delivery algorithm for latent class identificati... more This study explored a computerized adaptive test delivery algorithm for latent class identification based on the mixture Rasch model. Four item selection methods based on the Kullback–Leibler (KL) information were proposed and compared with the reversed and the adaptive KL information under simulated testing conditions. When item separation was large, all item selection methods did not differ evidently in terms of accuracy in classifying examinees into different latent classes and estimating latent ability. However, when item separation was small, two methods with class-specific ability estimates performed better than the other two methods based on a single latent ability estimate across all latent classes. The three types of KL information distributions were compared. The KL and the reversed KL information could be the same or different depending on the ability level and the item difficulty difference between latent classes. Although the KL information and the reversed KL informati...
Journal of Modern Applied Statistical Methods
investigated the issues of singularities and local maximum solutions within growth mixture models... more investigated the issues of singularities and local maximum solutions within growth mixture models (GMMs) and made recommendations regarding the use of multiple starting values. Building on their work, this simulation study investigates the feasibility of estimating GMMs within Mplus as measured by convergence to proper, but local solutions.
Journal of Modern Applied Statistical Methods
investigated the issues of singularities and local maximum solutions within growth mixture models... more investigated the issues of singularities and local maximum solutions within growth mixture models (GMMs) and made recommendations regarding the use of multiple starting values. Building on their work, this simulation study investigates the feasibility of estimating GMMs within Mplus as measured by convergence to proper, but local solutions.
Http Dx Doi Org 10 1207 S15324818ame0303_1, Dec 14, 2009
ABSTRACT This article demonstrates the usefulness of latent class modeling in addressing several ... more ABSTRACT This article demonstrates the usefulness of latent class modeling in addressing several measurement issues, particularly those related to hierarchical structures among skills. A study is described that explores a variety of previously proposed hypotheses regarding the structural relations among multiple-choice items used in the assessment of reading comprehension. The posited relations investigated were either compatible with a holistic or a subskill view of reading comprehension. Two types of literal comprehension items (tapping important and unimportant information) and two types of inferential comprehension items (within-sentence inferences and main idea inferences) were assessed relative to various hierarchical relation models. For two respondent groups (good and poor readers), all item types appeared to be measures of a single underlying atttribute. Furthermore, evidence indicated that reader groups differed in the latent proportion of acquirers of the underlying attribute. Finally, in terms of error rates, particular items and passages appeared to be better than others for assessing individuals with regard to the attribute.
The Pearson.and likelihood ratio statistics are c frequently used for assessing the absolute fit ... more The Pearson.and likelihood ratio statistics are c frequently used for assessing the absolute fit of probability models. Researchers are often interested in comparing fits provided by different models which may have a subsuming or .non-subsuming relation. A subsuming relation exists when the:parameters of the riduced model form_a_!tubset of those contained in the subsuming, or full, model: A non-subsuming relation exists when the defining parameters in neither model form a subset of those defining the other model. A general "mixture" probability model which incorporates two non-subsuming probability models and a strategy for as §essing fit provided by each of.the component models is described. A detailed , description of the strategy for selecting a preferred model is outlined. Applications of the suggested procedure are considered for the special case in which the Rasch latent trait model and Latent State Mastery model are compared as to relative preference when data are generated from each.model. (DWH) '\N A "mixture" probability model which incorporates two psycho-.rmetric models frOm separate parametric families is introduced and the application of this model in selecting a preferred component model is described. Example applications of the suggested procedure are L considered for the special casein which the Rasch latent trait model and the Latent State Mastery model are compared as to their relative preference when data .are generated from each of these moilels. 7 e." del NT'
... A/k, with eqZtl ltte0t Zlt1 t1retti101 Z11 1111 M\ c,. ith eqZtl ZO et1s1 ind eqZtl ltte0t Zl... more ... A/k, with eqZtl ltte0t Zlt1 t1retti101 Z11 1111 M\ c,. ith eqZtl ZO et1s1 ind eqZtl ltte0t Zlt1 t1t1tti1n1 Z11 1111 17.69 21.07 39.03 t. 37 41.89 Zo 25. ... Xx 0.17 0.13 0.20 0.27 0. t G11 1 (E11) G11 2 (Smith) G11 3 (Fsie0d) G11 1 (E11) G11 2 (Smith) G11 3 (Fsie0d) Patametet ZUC t1b1. ...
A probabilistichypothesis testing. procedure-..to. -assess the'.-fit.of hypothesized hierarchical... more A probabilistichypothesis testing. procedure-..to. -assess the'.-fit.of hypothesized hierarchical -structuresfortest item data. is.discussed. Statistical procedures are presented which areuseful for-evaluating the fit-of data-.of-a-certain. ClaSs of probabilistic-models. These models apply to-sets:of diChOtoious (0,1) responses for which there are posited-to exist a priotidependence structures. Examples of relevant types of data-..are succeSs/failurg .patterns from-Piagetian-tiskS, learning hierarchies, and domain . referenoed.tests,-.as-mell as agree/disagree,responSes. from attitude tests. _author/RC)
Psychometrika, Feb 1, 1992
This paper provides a description of a new adaptive testing algorithm based on a latent class mod... more This paper provides a description of a new adaptive testing algorithm based on a latent class modeling framework. The algorithm incorporates a four-stage iterative procedure that conditionally minimizes expected loss in classification of respondents across different content domains. The classification decisions relate to the membership of a person in a category of a latent variable for each of the separate domains considered. The algorithm appears to be particularly effective when latent class membership is related across the various domains of interest, since classification decisions on domains assessed early in the process are used to revise the probabilities for latent class membership on domains for which classification decisions have not yet been made. To assess the effectiveness of the proposed algorithm, a simulation based upon real data was conducted. For this example, the algorithm proved to be relatively efficient, requiring only 40% of the number of items needed under a nonadaptive approach. In addition, the algorithm provided classification decisions which, in 96% of the cases, were consistent with decisions based upon all available items when the maximum acceptable classification error rate was set at 5%.
When latent class parameters are estimated, maximum likelihood and Pearson chi-square statistics ... more When latent class parameters are estimated, maximum likelihood and Pearson chi-square statistics can be derived for assessing the fit of the model to the data. This study used simulated data to compare these two statistics, and is based on mixtures of latent binomial distributions, using data generated from five dichotomous manifest variables. Data were generated for a two-class unconstrained model and a three-class constrained model. Data were also generated ender three independent variables--sample size and two param,ters that define latent class models (conditional response probability and latent class proportion). Parameters were estimated for the generation models and a series of subsumed and subsuming models. Maximum likelihood and Pearson chi-square statistics were derived for each estimation. Distributions of fit statistics were produced by 1,000 replications. For each distribution of statistics, the overall fit to the appropriate chi-square distribution was assessed. In addition, the mean, variance, and tail weights were examined. The distributions of the statistics varied according to the parameter values of the models and the type of models estimated. When the estimated model accurately reflected the data, the Pearson statistic was generally distributed as a chi-square for both large and small samples, while the maximum likelihood statistic was distributed as a chi-square only at the large sample size. Fourteen tables of supporting statistics are included.
presents a latent class conceptualization of longitudinal data as they might arise in social scie... more presents a latent class conceptualization of longitudinal data as they might arise in social science settings / to provide a systematic basis for model building, the modeling has been divided into 2 stages / during the 1st stage, referred to as within-occasions, an effort is made to locate one, or a related set of 2 or more, reasonable latent class models for the acquisition of the skills represented at each occasion / although the term acquisition has been utilized in this context since our primary focus has been on modeling development of skills in academic settings, generalization to other situations is straightforward / at the 2nd stage of modeling, the focus is on change over time / in the present context, this was described as migration between acquisition states / selecting an appropriate latent class model involves comparisons among competing models / illustrate—and argue for—the potential usefulness of the Akaike minimum AIC [Akaike information criterion] procedure focus . ...
Applied Measurement in Education, 1990
ABSTRACT This article demonstrates the usefulness of latent class modeling in addressing several ... more ABSTRACT This article demonstrates the usefulness of latent class modeling in addressing several measurement issues, particularly those related to hierarchical structures among skills. A study is described that explores a variety of previously proposed hypotheses regarding the structural relations among multiple-choice items used in the assessment of reading comprehension. The posited relations investigated were either compatible with a holistic or a subskill view of reading comprehension. Two types of literal comprehension items (tapping important and unimportant information) and two types of inferential comprehension items (within-sentence inferences and main idea inferences) were assessed relative to various hierarchical relation models. For two respondent groups (good and poor readers), all item types appeared to be measures of a single underlying atttribute. Furthermore, evidence indicated that reader groups differed in the latent proportion of acquirers of the underlying attribute. Finally, in terms of error rates, particular items and passages appeared to be better than others for assessing individuals with regard to the attribute.
The use of loglinear latent class models to detect item biap was studied. Purposes of the study w... more The use of loglinear latent class models to detect item biap was studied. Purposes of the study were to: (1) develop procedurts for use in assessing item bias when the grouping variable with respect,to which bias occurs is not observed; (2) develop bias detection procedures that relate to a conceptually different assessed trait--a categorical attribute; and (3) exemplify the use of these developed procedures with real world data. Models are formulated so that the attribute to be measured may be continuous, as in a Rasch model, or categorical, as in latent class models. The item bias to be studied may correspond to a manifest grouping variable, a latent grouping variable, or both. Likelihood-ratio tests for assessing the presence of various types of bias are described. These methods are illustrated through analysis of a "real world" data set from a study of multiplication items administered to 286 Dutch undergraduates. Bias was related to a manifest grouping variable by giving 143 of the subjects some training in Roman numerals, in which some of the multiplication problems were written. Results indicate that it was possible to explain item bias through differences in item difficulties or error rates across levels of grouping variables. The model represented can be extended to include several observed and unobserved variables. Ten tables present information about the models and findings of the study. A 39-item list of references is included.
Journal of Speech Language and Hearing Research, 1983
The internal consistency, variability, and performance level of 50 deaf and 50 hearing subjects (... more The internal consistency, variability, and performance level of 50 deaf and 50 hearing subjects (with comparable SAT reading comprehension scores) were compared on two production (cloze and free-response) tasks and two recognition (multiple-choice and modified-cloze) tasks. Multiple-choice and free-response tasks were administered under both lookback and no-lookback conditions. Task consistencies and variabilities for deaf and hearing groups did not differ appreciably. Groups differed, however, with respect to mean level of performance. Deaf subjects' overall task performance level tended to be lower than that of hearing subjects, with the greatest differences noted in lookback and production conditions.
Journal of Experimental Psychology, 1974
ABSTRACT Found that under analogous transformations 2nd and 3rd graders (N = 64) tended to conser... more ABSTRACT Found that under analogous transformations 2nd and 3rd graders (N = 64) tended to conserve both their own and another person's weight prior to conserving the weight of nonhuman objects (a rubber doll and a piece of clay). Findings suggest that children acquire conservation of weight in a sequential manner, with the type of object used in a conservation task affecting the time when conservation is first observed. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Applied Latent Class Analysis, 2002
... A/k, with eqZtl ltte0t Zlt1 t1retti101 Z11 1111 M\ c,. ith eqZtl ZO et1s1 ind eqZtl ltte0t Zl... more ... A/k, with eqZtl ltte0t Zlt1 t1retti101 Z11 1111 M\ c,. ith eqZtl ZO et1s1 ind eqZtl ltte0t Zlt1 t1t1tti1n1 Z11 1111 17.69 21.07 39.03 t. 37 41.89 Zo 25. ... Xx 0.17 0.13 0.20 0.27 0. t G11 1 (E11) G11 2 (Smith) G11 3 (Fsie0d) G11 1 (E11) G11 2 (Smith) G11 3 (Fsie0d) Patametet ZUC t1b1. ...
Latent Trait and Latent Class Models, 1988
Handbook of Statistics, 2006
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Papers by George Macready