scholarly journals Lord–Wingersky Algorithm Version 2.0 for Hierarchical Item Factor Models with Applications in Test Scoring, Scale Alignment, and Model Fit Testing

Psychometrika ◽  
2014 ◽  
Vol 80 (2) ◽  
pp. 535-559 ◽  
Author(s):  
Li Cai
Psychometrika ◽  
2021 ◽  
Author(s):  
Sijia Huang ◽  
Li Cai

AbstractItem response theory scoring based on summed scores is employed frequently in the practice of educational and psychological measurement. Lord and Wingersky (Appl Psychol Meas 8(4):453–461, 1984) proposed a recursive algorithm to compute the summed score likelihood. Cai (Psychometrika 80(2):535–559, 2015) extended the original Lord–Wingersky algorithm to the case of two-tier multidimensional item factor models and called it Lord–Wingersky algorithm Version 2.0. The 2.0 algorithm utilizes dimension reduction to efficiently compute summed score likelihoods associated with the general dimensions in the model. The output of the algorithm is useful for various purposes, for example, scoring, scale alignment, and model fit checking. In the research reported here, a further extension to the Lord–Wingersky algorithm 2.0 is proposed. The new algorithm, which we call Lord–Wingersky algorithm Version 2.5, yields the summed score likelihoods for all latent variables in the model conditional on observed score combinations. The proposed algorithm is illustrated with empirical data for three potential application areas: (a) describing achievement growth using score combinations across adjacent grades, (b) identification of noteworthy subscores for reporting, and (c) detection of aberrant responses.


2020 ◽  
Vol 46 (Supplement_1) ◽  
pp. S179-S179
Author(s):  
Mei San Ang ◽  
Gurpreet Rekhi ◽  
Jimmy Lee

Abstract Background The conceptualization of negative symptoms has been refined in the past decades. Two-factor model comprising Motivation and Pleasure (MAP) and Emotional Expressivity (EE), five-factor model representing five domains of negative symptoms and second-order five-factor model incorporating the two-factor and five-factor models (Anhedonia, Asociality and Avolition regressed on MAP; Blunted Affect and Alogia regressed on EE) have been suggested as latent structure of negative symptoms. In most studies, the item “Lack of Normal Distress” in the Brief Negative Symptom Scale (BNSS) did not fit well in factor models. Nevertheless, the reported correlation and item-total correlation of Distress with other negative symptom domains and BNSS items were not negligible. Emotion deficit was also discussed as a part of negative symptoms conceptualization. As a single item may not be sufficient to represent an underlying construct that is potentially abstract and complex, the Schedule for the Deficit Syndrome (SDS) which comprises “Diminished Emotional Range” that is conceptually relevant to the BNSS Distress was employed. The study aimed to reexamine the conceptualization of negative symptoms by examining the model fit of several models when BNSS Distress and SDS Emotion (EMO) were included in the models using confirmatory factor analyses (CFA). Methods Two-hundred and seventy-four schizophrenia outpatients aged 21–65 were assessed on the BNSS and SDS. In the two-factor models, Restricted Affect, Diminished Emotional Range and Poverty of Speech in SDS and all items in BNSS Blunted Affect and Alogia subscales were regressed on EE, Curbing of Interests, Diminished Sense of Purpose and Diminished Social Drive in SDS and all items in BNSS Anhedonia, Asociality and Avolition subscales were regressed on MAP, without EMO, or with EMO regressed on either EE or MAP. Five-factor models and second-order five-factor models were examined, with or without EMO. Lastly, a six-factor model with EMO manifested by the sixth factor and second-order six-factor models in which EMO was regressed on either EE or MAP were tested. Root mean square error of approximation (RMSEA) <0.08, comparative fit index (CFI) >0.95, the Tucker-Lewis Index (TLI) >0.95, and weighted root-mean-square residual (WRMR) <1.0 indicate good model fit. CFAs were conducted using Mplus version 7.4. Results The two-factor models did not yield adequate fit indices. Five-factor model and second-order five-factor model without EMO had good model fit; five-factor model: RMSEA=0.056 (0.044–0.068), CFI=0.996, TFI=0.995, WRMR=0.718; second-order five-factor model: RMSEA=0.049 (0.036–0.061), CFI=0.997, TFI=0.996, WRMR=0.758. When EMO was included as indicator in one of the factors in the five-factor models, only the model in which EMO was regressed on Alogia yielded adequate fit. Similarly, in the second-order five-factor models, adequate fit indices were observed only when EMO was regressed on Alogia and Blunted Affect. The six-factor model fitted the data well, RMSEA=0.053 (0.042–0.064), CFI=0.996, TFI=0.995, WRMR=0.711. Second-order six-factor model with EMO regressed on EE yielded better model fit than MAP, RMSEA=0.050 (0.039–0.061), CFI=0.996, TFI=0.995, WRMR=0.849. Discussion In line with previous studies, five-factor and second-order five-factor models without EMO fitted the data well. When EMO was included, a six-factor model and a second-order six-factor model in which the sixth factor was regressed on EE showed good model fit. Emotion, motivation and behavior are intertwined. Our results showed that diminished emotion may also be one of the components of negative symptoms, which had higher association with EE than MAP.


2020 ◽  
pp. 107769902095240 ◽  
Author(s):  
Guangchao Charles Feng ◽  
Xianglin Su ◽  
Zhiliang Lin ◽  
Yiru He ◽  
Nan Luo ◽  
...  

Examining the determinants of technology acceptance has been a central interest across disciplines. The technology acceptance model (TAM) and its variants and extensions are the most popular theoretical frameworks in this line of research. Two model-based meta-analytical approaches, that is, meta-meta-analysis and conventional meta-analysis, are used to pool the correlations and to test the path relationships among the variables of the TAM. We find that the extended TAM, which we term the TAM Plus, prevails in the model fit testing and that the results of the pooled correlations and path coefficients estimated using the meta-meta-analysis and meta-analysis are generally consistent.


Author(s):  
Afni Sirait ◽  
Ida Ayu Purnama

Technology is a necessity that cannot be separated from life today. Daily activities are made easier and even dismiss distance, space, and time. This convenience provides cost savings, increases time use quality, and even changes a business process. This study aims to analyze the model of consumer behavior of generation X in the use of digital transactions. This research is a quantitative approach with 73 respondents who fit the qualifications. The data was collected using a questionnaire which was then tested for validity, reliability, and model fit using the WarpPLS 6.0 analysis tool. The test results explained that consumption behavior mediated cultural factors do not directly affect the generation of digital transaction X (the value path coefficient H1 equals -0007 P = 0,28). Psychological factors have a direct influence on digital transactions Generation X (H2 has a value of path coefficients 0,12 and P = 0,15), but it has indirect influence the results of the mediation of the variable consumption behavior against the decision transaction generation digital X (the value path coefficient 0.728, P<0.001, and R-Squared 0.57) with the model fit testing the VIF value of 1.236, and the GoF value of 0.411. The limitation of this study is that the population only focuses on generation X.


2018 ◽  
Author(s):  
Mijke Rhemtulla ◽  
Riet van Bork ◽  
Denny Borsboom

Previous research and methodological advice has focused on the importance of accounting for measurement error in psychological data. That perspective assumes that psychological variables conform to a common factor model, such that they consist of construct variance plus error. In this paper, we explore what happens when a set of items that are not generated from a common factor construct model are nonetheless modeled as reflecting a common factor. Through a series of hypothetical examples and an empirical re-analysis, we show that (1) common factor models tend to produce extremely biased and highly variable structural parameter estimates when the population model is not a common factor model; (2) model fit is a poor indicator of the degree of bias; and (3) composite models are sometimes more reliable than common factor models under alternative measurement structures, though they also lead to unacceptably bad solutions in some cases.


1989 ◽  
Vol 26 (1) ◽  
pp. 105-111 ◽  
Author(s):  
Paula Fitzgerald Bone ◽  
Subhash Sharma ◽  
Terence A. Shimp

The authors propose a bootstrap procedure for evaluating the goodness-of-fit indices for structural equation and confirmatory factor models. Monté Carlo simulations are applied to obtain a bootstrap sampling distribution (BSD) for each fit statistic. Then the BSD is used to evaluate model fit. Because the BSD takes into consideration sample size and model characteristics (e.g., number of factors, number of indicators per factor), its application in the proposed procedure makes it possible to compare the fits of competing models. Two previous studies are reanalyzed in illustrating how to implement the proposed procedure.


2021 ◽  
Author(s):  
Ewan Carr ◽  
Silia Vitoratou ◽  
Trudie Chalder ◽  
Kimberley Goldsmith

AbstractBackgroundWhen measuring latent traits, such as those used in psychology and psychiatry, it can be unclear whether the instruments used are measuring different concepts. This issue is particularly important in context of mediation analysis, since for a sound mediation hypothesis the mediator and outcome should be distinct. We sought to assess the extent of measurement overlap between mediators and outcomes in the PACE trial (n=640).MethodsPotential measurement overlap was assessed using generalised linear latent variable models where confirmatory factor models quantified the extent to which the addition of cross-loading items resulted in significant improvements in model fit.ResultsOut of 26 mediator-outcome pairs considered, only six showed evidence of cross-loading items, supporting the suggestion that mediator and outcome constructs in the PACE trial were conceptually distinct.ConclusionsThis study highlights the importance of assessing measurement overlap in mediation analyses with latent traits to ensure mediator and outcome instruments are distinct.


2021 ◽  
Author(s):  
Melissa Gordon Wolf ◽  
Daniel McNeish

Assessing unidimensionality of a scale is a frequent interest in behavioral research. Often, this is done with approximate model fit indices in a factor analysis framework such as RMSEA, CFI, or SRMR. These fit indices are continuous measures, so values indicating acceptable fit are up to interpretation. Cutoffs suggested by Hu and Bentler (1999) are a common guideline used in empirical research. However, these cutoffs were derived with intent to detect omitted cross-loadings or omitted factor covariances in three-factor models. These types of misspecifications cannot exist in one-factor models, so the appropriateness of using these guidelines in one-factor models is uncertain. This paper uses a simulation study to address whether traditional fit index cutoffs are sensitive to the types of misspecifications that can occur in one-factor models. The results showed that traditional cutoffs have very poor sensitivity to misspecification in one-factor models and that the traditional cutoffs generalize poorly to one-factor contexts. As an alternative, we investigate the accuracy and stability of the recently introduced dynamic fit cutoff approach for creating fit index cutoffs for one-factor models. Simulation results indicated excellent performance of dynamic fit index cutoffs to classify correct or misspecified one-factor models and that dynamic fit index cutoffs are a promising approach for more accurate assessment of unidimensionality.


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