scholarly journals Effect of Dichotomization on the Latent Structure of Data

2021 ◽  
Vol 7 ◽  
Author(s):  
Karl Schweizer ◽  
Andreas Gold ◽  
Dorothea Krampen
Keyword(s):  
Simulation Study ◽  
Latent Variables ◽  
Latent Variable ◽  
Factor Model ◽  
Latent Structure ◽  
Factor Loadings ◽  
Dichotomous Data ◽  
Level Data ◽  
Confirmatory Factor

We investigated whether dichotomous data showed the same latent structure as the interval-level data from which they originated. Given constancy of dimensionality and factor loadings reflecting the latent structure of data, the focus was on the variance of the latent variable of a confirmatory factor model. This variance was shown to summarize the information provided by the factor loadings. The results of a simulation study did not reveal exact correspondence of the variances of the latent variables derived from interval-level and dichotomous data but shrinkage. Since shrinkage occurred systematically, methods for recovering the original variance were fleshed out and evaluated.

scholarly journals Can Variances of Latent Variables be Scaled in Such a Way That They Correspond to Eigenvalues?

2017 ◽  
Vol 6 (6) ◽  
pp. 35 ◽  
Author(s):  
Karl Schweizer ◽  
Stefan Troche ◽  
Siegbert Reiß
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Simulation Study ◽  
Latent Variables ◽  
Latent Variable ◽  
Factor Model ◽  
Estimation Method ◽  
Factor Loadings ◽  
Confirmatory Factor ◽  
Theoretical Foundations

The paper reports an investigation of whether sums of squared factor loadings obtained in confirmatory factor analysis correspond to eigenvalues of exploratory factor analysis. The sum of squared factor loadings reflects the variance of the corresponding latent variable if the variance parameter of the confirmatory factor model is set equal to one. Hence, the computation of the sum implies a specific type of scaling of the variance. While the investigation of the theoretical foundations suggested the expected correspondence between sums of squared factor loadings and eigenvalues, the necessity of procedural specifications in the application, as for example the estimation method, revealed external influences on the outcome. A simulation study was conducted that demonstrated the possibility of exact correspondence if the same estimation method was applied. However, in the majority of realized specifications the estimates showed similar sizes but no correspondence. 

The EV Scaling Method for Variances of Latent Variables

Methodology ◽  
2019 ◽  
Vol 15 (4) ◽  
pp. 175-184
Author(s):  
Karl Schweizer ◽  
Stefan Troche
Keyword(s):  
Simulation Study ◽  
Empirical Data ◽  
Latent Variables ◽  
Factor Models ◽  
Scaling Method ◽  
Factor Loadings ◽  
Confirmatory Factor ◽  
Variance Parameters ◽  
Second Procedure ◽  
Estimation Of Variance

Abstract. The paper describes EV scaling for variances of latent variables included in confirmatory factor models. EV-scaled variances can be achieved in two ways: the estimation of variance parameters based on adjusted factor loadings and alternatively the summation of squared factor loadings obtained under the condition that the variance parameter is set equal to one. By definition, the second procedure yields values that are always positive. EV-scaled variances of latent variables show sizes similar to eigenvalues. The outcome of applying this scaling method is demonstrated in empirical data. The results of a simulation study reveal that the outcomes of the two ways virtually always correspond if the data are generated to include the contribution of a latent source. If there is no such source, the exclusion of solutions with negative error variances virtually always leads to correspondence.

scholarly journals On Modeling Missing Data of an Incomplete Design in the CFA Framework

2020 ◽  
Vol 11 ◽  
Author(s):  
Karl Schweizer ◽  
Andreas Gold ◽  
Dorothea Krampen ◽  
Tengfei Wang
Keyword(s):  
Missing Data ◽  
Latent Variable ◽  
Binary Data ◽  
Factor Model ◽  
Model Fit ◽  
Negative Effects ◽  
Factor Loadings ◽  
Confirmatory Factor ◽  
The Hierarchical Structure ◽  
Incomplete Design

The paper reports an investigation on whether valid results can be achieved in analyzing the structure of datasets although a large percentage of data is missing without replacement. Two types of confirmatory factor analysis (CFA) models were employed for this purpose: the missing data CFA model with an additional latent variable for representing the missing data and the semi-hierarchical CFA model that also includes the additional latent variable and reflects the hierarchical structure assumed to underlie the data. Whereas, the missing data CFA model assumes that the model is equally valid for all participants, the semi-hierarchical CFA model is implicitly specified differently for subgroups of participants with and without omissions. The comparison of these models with the regular one-factor model in investigating simulated binary data revealed that the modeling of missing data prevented negative effects of missing data on model fit. The investigation of the accuracy in estimating the factor loadings yielded the best results for the semi-hierarchical CFA model. The average estimated factor loadings for items with and without omissions showed the expected equal sizes. But even this model tended to underestimate the expected values.

Probability-Based and Measurement-Related Hypotheses With Full Restriction for Investigations by Means of Confirmatory Factor Analysis

Methodology ◽  
2011 ◽  
Vol 7 (4) ◽  
pp. 157-164
Author(s):  
Karl Schweizer
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Cognitive Processing ◽  
Latent Variables ◽  
Repeated Measures ◽  
Latent Variable ◽  
Model Fit ◽  
Repeated Measures Data ◽  
Confirmatory Factor ◽  
And Performance

Probability-based and measurement-related hypotheses for confirmatory factor analysis of repeated-measures data are investigated. Such hypotheses comprise precise assumptions concerning the relationships among the true components associated with the levels of the design or the items of the measure. Measurement-related hypotheses concentrate on the assumed processes, as, for example, transformation and memory processes, and represent treatment-dependent differences in processing. In contrast, probability-based hypotheses provide the opportunity to consider probabilities as outcome predictions that summarize the effects of various influences. The prediction of performance guided by inexact cues serves as an example. In the empirical part of this paper probability-based and measurement-related hypotheses are applied to working-memory data. Latent variables according to both hypotheses contribute to a good model fit. The best model fit is achieved for the model including latent variables that represented serial cognitive processing and performance according to inexact cues in combination with a latent variable for subsidiary processes.

Study of the Factor Structure, Profiles, and Concurrent Validity of the Mindset Assessment Profile Tool for Elementary Students

2020 ◽  
pp. 073428292094345
Author(s):  
Yaacov Petscher ◽  
Stephanie Al Otaiba ◽  
Jeanne Wanzek
Keyword(s):  
Reading Comprehension ◽  
Concurrent Validity ◽  
Word Reading ◽  
Factor Model ◽  
Latent Structure ◽  
Future Research ◽  
Standardized Measures ◽  
Fourth Grade Students ◽  
Confirmatory Factor ◽  
High Effort

This study explored the underlying latent structure of items on the Mindset Assessment Profile (MAP) tool, explored whether subgroups of students exist based on the latent structure of MAP items, and tested whether subgroups were differentiated on standardized measures of reading comprehension, vocabulary, and word reading. Participants included 431 fourth-grade students. Confirmatory factor analysis revealed that a three-factor model provided the most parsimonious fit to the data. Results of exploratory finite mixture model analysis with auxiliary regression suggested five classes of students, with the students categorized as growth mindset—high effort profile having the highest observed reading comprehension ( M = 451.98 and SD = 38.88) and vocabulary ( M = 454.37 and SD = 34.74) scores. By contrast, students categorized as fixed mindset—higher effort had the lowest observed reading comprehension and vocabulary scores. Limitations and directions for future research, and implications for using MAP assessment to inform intervention are discussed.

scholarly journals On the Equivalency of Factor and Network Loadings

2020 ◽  
Author(s):  
Alexander P. Christensen ◽  
Hudson Golino
Keyword(s):  
Factor Model ◽  
Network Models ◽  
High Sensitivity ◽  
Factor Loading ◽  
Random Factor ◽  
Factor Loadings ◽  
Network Measure ◽  
Confirmatory Factor ◽  
Similar Information ◽  
Loading Matrix

Recent research has demonstrated that the network measure node strength or sum of a node’s connections is roughly equivalent to confirmatory factor analysis (CFA) loadings. A key finding of this research is that node strength represents a combination of different latent causes. In the present research, we sought to circumvent this issue by formulating a network equivalent of factor loadings, which we call network loadings. In two simulations, we evaluated whether these network loadings could effectively (1) separate the effects of multiple latent causes and (2) estimate the simulated factor loading matrix of factor models. Our findings suggest that the network loadings can effectively do both. In addition, we leveraged the second simulation to derive effect size guidelines for network loadings. In a third simulation, we evaluated the similarities and differences between factor and network loadings when the data were generated from random, factor, and network models. We found sufficient differences between the loadings, which allowed us to develop an algorithm to predict the data generating model called the Loadings Comparison Test (LCT). The LCT had high sensitivity and specificity when predicting the data generating model. In sum, our results suggest that network loadings can provide similar information to factor loadings when the data are generated from a factor model and therefore can be used in a similar way (e.g., item selection, measurement invariance, factor scores).

The confirmatory factor analysis of teacher’s research motivation scale

2018 ◽  
Vol 8 (3) ◽  
pp. 101-106
Author(s):  
Ujsara Prasertsin
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Intrinsic Motivation ◽  
Latent Variables ◽  
Latent Variable ◽  
Extrinsic Motivation ◽  
Class Action ◽  
P Value ◽  
Confirmatory Factor ◽  
Motivation Scale

The purpose of the research is to develop the measurement of motivation scale of in class action research conducted by school teachers. The sampling is 403 teachers, subordinated to Office of The Basic Education Commission. Data collection was conducted through questionnaires of 20 questions. The questions were designed into 5 levels following to the motivation scale in research measurement of Deemer, Mahoney, & Ball (2010). This 20 questions questionnaire is consisting of 3 latent variables that are 9 questions of intrinsic motivation, 6 questions of failure avoidance and 5 questions extrinsic motivation. The purpose of confirmatory factor analysis (CFA) is to test the construct validity of research latent variables that found the harmony correlation of empirical data contained in this research model, the value of Chi-Square ( )=89.224 at the degree of freedom=71, P value=0.071, GFI=0.978, AGFI=0.936, RMSEA=0.062, RMR=0.018, Model AIC=367.224, Saturated AIC=420.000, Model CAIC= 1062.076, Saturated CAIC = 1469.777. The weight factors of latent variable are 0.692, -0.066 and 0.894 retrospectively. The value of reliability according to cronbach’s alpha coefficient of correlation is 0.479, 0.004 and 0.800 retrospectively. Moreover correlation matrix of 20 observed variables shows the correlation among latent variables of intrinsic motivation and extrinsic motivation with the significant level of statistic correlation at 0.05, the correlation value ranged between 0.196-0.604 and 0.196-0.696 retrospectively. The highest value of correlation scored 0.696 is founded in observed variables of intrinsic motivation latent variable. Keywords: Confirmatory, factor analysis, teacher, research motivation

Latent Structure of the Social Interaction Self-Statement Test: An Application of Hierarchical Confirmatory Factor Analysis

1999 ◽  
Vol 84 (3_suppl) ◽  
pp. 1303-1314 ◽  
Author(s):  
Sehee Hong ◽  
Yongrae Cho
Keyword(s):  
Social Interaction ◽  
Factor Model ◽  
Factor Models ◽  
Latent Structure ◽  
Test Results ◽  
Factor Analyses ◽  
Confirmatory Factor Analyses ◽  
The Social ◽  
Confirmatory Factor ◽  
Order Factor

Since the Social Interaction Self-statement Test was presented, a clear factor structure of the measure has not been defined. This situation is largely due to a lack of agreement among researchers with respect to the method of factoring, rotation criteria, and interpretation of factor loadings. The aim of the present study was to evaluate, using confirmatory factor analyses, the various factor models of the test. Results clearly supported a novel second-order factor model, which was developed by combining the current two- and five-factor models.

scholarly journals Quantifying the Core Deficit in Classical Schizophrenia

2020 ◽  
Vol 1 (1) ◽  
Author(s):  
Mohanbabu Rathnaiah ◽  
Elizabeth B Liddle ◽  
Lauren Gascoyne ◽  
Jyothika Kumar ◽  
Mohammad Zia Ul Haq Katshu ◽  
...  
Keyword(s):  
Latent Variable ◽  
Factor Model ◽  
Mental Activity ◽  
Brain Disorders ◽  
Role Function ◽  
The Core ◽  
Core Deficit ◽  
Confirmatory Factor ◽  
Predicting Outcome ◽  
Impaired Cognition

Abstract In the classical descriptions of schizophrenia, Kraepelin and Bleuler recognized disorganization and impoverishment of mental activity as fundamental symptoms. Their classical descriptions also included a tendency to persisting disability. The psychopathological processes underlying persisting disability in schizophrenia remain poorly understood. The delineation of a core deficit underlying persisting disability would be of value in predicting outcome and enhancing treatment. We tested the hypothesis that mental disorganization and impoverishment are associated with persisting impairments of cognition and role function, and together reflect a latent core deficit that is discernible in cases diagnosed by modern criteria. We used Confirmatory Factor Analysis to determine whether measures of disorganization, mental impoverishment, impaired cognition, and role functioning in 40 patients with schizophrenia represent a single latent variable. Disorganization scores were computed from the variance shared between disorganization measures from 3 commonly used symptom scales. Mental impoverishment scores were computed similarly. A single factor model exhibited a good fit, supporting the hypothesis that these measures reflect a core deficit. Persisting brain disorders are associated with a reduction in post-movement beta rebound (PMBR), the characteristic increase in electrophysiological beta amplitude that follows a motor response. Patients had significantly reduced PMBR compared with healthy controls. PMBR was negatively correlated with core deficit score. While the symptoms constituting impoverished and disorganized mental activity are dissociable in schizophrenia, nonetheless, the variance that these 2 symptom domains share with impaired cognition and role function, appears to reflect a pathophysiological process that might be described as the core deficit of classical schizophrenia.

scholarly journals A Comparison of Methods for Estimating Relationships in the Change Between Two Time Points for Latent Variables

2016 ◽  
Vol 78 (2) ◽  
pp. 232-252 ◽  
Author(s):  
W. Holmes Finch ◽  
Sungok Serena Shim
Keyword(s):  
Simulation Study ◽  
Latent Variables ◽  
Factor Model ◽  
Latent Trait ◽  
Factor Loading ◽  
Change Score ◽  
Standard Errors ◽  
Time Points ◽  
Complex Relationships ◽  
Latent Traits

Collection and analysis of longitudinal data is an important tool in understanding growth and development over time in a whole range of human endeavors. Ideally, researchers working in the longitudinal framework are able to collect data at more than two points in time, as this will provide them with the potential for a deeper understanding of the development processes under study and a much broader array of statistical modeling options. However, in some circumstances data collection is limited to only two time points, perhaps because of resource limitations, issues with the context in which the data are collected, or the nature of the trait under study. In such instances, researchers may still want to learn about complex relationships in the data, such as the correlation between changes in latent traits that are being measured. However, with only two data points, standard approaches for modeling such relationships, such as growth curve modeling, cannot be used. The current simulation study compares the performance of two methods for estimating the correlations among changes in latent variables between two points in time, the two-wave latent change score model and the latent difference factor model. Results of the simulation study showed that both methods yielded generally accurate estimates of the correlation between changes in a latent trait, with relatively small standard errors. Estimation bias and standard errors were lower with larger samples, larger factor loading magnitudes, and more indicators per factor. Further comparisons between the methods and implications of these results are discussed.

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