Correcting the Bias of the Root Mean Squared Error of Approximation under Missing Data

Missing data are ubiquitous in both small and large datasets. Missing data may come about as a result of coding or computer error, participant absences, or it may be intentional, as in planned missing designs. We discuss missing data as it relates to goodness-of-fit indices in Structural Equation Modeling (SEM), specifically the effects of missing data on the Root Mean Squared Error of Approximation (RMSEA). We use simulations to show that naive implementations of the RMSEA have a downward bias in the presence of missing data and, thus, overestimate model goodness-of-fit. Unfortunately, many state-of-the-art software packages report the biased form of RMSEA. As a consequence, the community may have been accepting a much larger fraction of models with non-acceptable model fit. We propose a bias-correction for the RMSEA based on information-theoretic considerations that take into account the expected misfit of a person with fully observed data. This results in an RMSEA which is asymptotically independent of the proportion of missing data for misspecified models. Importantly, results of the corrected RMSEA computation are identical to naive RMSEA if there are no missing data.

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Correcting the bias of the Root Mean Squared Error of Approximation under missing data

Methodology ◽

10.5964/meth.2333 ◽

2021 ◽

Vol 17 (3) ◽

pp. 189-204

Author(s):

Cailey E. Fitzgerald ◽

Ryne Estabrook ◽

Daniel P. Martin ◽

Andreas M. Brandmaier ◽

Timo von Oertzen

Keyword(s):

Missing Data ◽

Structural Equation ◽

Goodness Of Fit ◽

Missing Values ◽

Mean Squared Error ◽

Psychological Research ◽

Equation Modeling ◽

Root Mean Squared Error ◽

Squared Error ◽

Downward Bias

Missing data are ubiquitous in psychological research. They may come about as an unwanted result of coding or computer error, participants' non-response or absence, or missing values may be intentional, as in planned missing designs. We discuss the effects of missing data on χ²-based goodness-of-fit indices in Structural Equation Modeling (SEM), specifically on the Root Mean Squared Error of Approximation (RMSEA). We use simulations to show that naive implementations of the RMSEA have a downward bias in the presence of missing data and, thus, overestimate model goodness-of-fit. Unfortunately, many state-of-the-art software packages report the biased form of RMSEA. As a consequence, the scientific community may have been accepting a much larger fraction of models with non-acceptable model fit. We propose a bias-correction for the RMSEA based on information-theoretic considerations that take into account the expected misfit of a person with fully observed data. The corrected RMSEA is asymptotically independent of the proportion of missing data for misspecified models. Importantly, results of the corrected RMSEA computation are identical to naive RMSEA if there are no missing data.

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Structural Equation Modeling: An Alternative to Traditional Validation Techniques

Journal of Educational Technology Systems ◽

10.2190/et14.4.j ◽

1986 ◽

Vol 14 (4) ◽

pp. 345-352

Author(s):

Margaret E. Bell ◽

Jean A. Massey

Keyword(s):

Structural Equation Modeling ◽

Structural Equation ◽

Goodness Of Fit ◽

Statistical Significance ◽

Equation Modeling ◽

Fit Indices ◽

T Values ◽

Conditions Of Learning ◽

Nursing Course ◽

Cardiovascular Nursing

Validation of the sequencing of objectives is an important step in structural design. Prior statistical techniques, such as the reproducibility coefficient, have yielded only summary information. In contrast, structural equation modeling provides both goodness-of-fit indices and effect coefficients for links or paths between time-ordered events, i.e., objectives. Discussed here is the application of structural equation modeling to a set of objectives in a senior-level cardiovascular nursing course. Consistent with the theory-based requirement of structural equation modeling, the objectives were developed using Robert Gagné's conditions of learning. Also discussed is the use of “t” values, which indicate statistical significance of the paths, for testing instructional links in the learning model.

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The Impact of BIB Spiraling-Induced Missing Data Patterns on Goodness-of-Fit Tests in Factor Analysis

Journal of Educational and Behavioral Statistics ◽

10.3102/10769986020001069 ◽

1995 ◽

Vol 20 (1) ◽

pp. 69-82 ◽

Cited By ~ 1

Author(s):

David Kaplan

Keyword(s):

Factor Analysis ◽

Missing Data ◽

Structural Equation ◽

Goodness Of Fit ◽

Covariance Matrices ◽

Equation Modeling ◽

Continuous Variables ◽

Goodness Of Fit Test ◽

New Approach ◽

The Impact

This article considers the impact of missing data arising from balanced incomplete block (BIB) spiraled designs on the chi-square goodness-of-fit test in factor analysis. Specifically, data arising from BIB designs possess a unique pattern of missing data that can be characterized as missing completely at random (MCAR). Standard approaches to factor analyzing such data rest on forming pairwise available case (PAC) covariance matrices. Developments in statistical theory for missing data show that PAC covariance matrices may not satisfy Wishart distribution assumptions underlying factor analysis, thus impacting tests of model fit. One approach, advocated by Muthén, Kaplan, and Hollis (1987) for handling missing data in structural equation modeling, is proposed as a possible solution to these problems. This study compares the new approach to the standard PAC approach in a Monte Carlo framework. Results show that tests of goodness-of-fit are very sensitive to PAC approaches even when data are MCAR, as is the case for BIB designs. The new approach is shown to outperform the PAC approach for continuous variables and is comparatively better for dichotomous variables.

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Mengakomodasi Efek Metode dalam Pengujian Validitas Konstruk Melalui Analisis Faktor Konfirmatori

Psikologia Jurnal Psikologi ◽

10.21070/psikologia.v1i1.478 ◽

2017 ◽

Vol 1 (1) ◽

pp. 37

Author(s):

Wahyu Widhiarso

Keyword(s):

Factor Analysis ◽

Confirmatory Factor Analysis ◽

Structural Equation ◽

Goodness Of Fit ◽

Equation Modeling ◽

Fit Indices ◽

Method Effect ◽

Confirmatory Factor ◽

Method Effects ◽

Item Writing

Literatures in the field of psychometrics recommend researchers to employvarious of methods on measuring individual attributes. Ideally,each methods are complementary and measuresthe construct designed to be measured. However, some problems arise when among the methods is unique and unrelated to the construct being measured. The uniqueness of method can lead what is called the method effect. In testing construct validity using confirmatory factor analysis, the emergence of this effect tend to reducing the goodness of fit indices of the model. There are many ways to solve these problem, one of themis controling the method effects and accommodate it to the model. This paper introduces how to accommodate method effecton the confirmatory factor analysis using structural equation modeling. In the application section, author identify the emergence of method effects due to the differences item writing direction (favorable-unfavorable). The analysis showed that method effectemerge from different writing direction.

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Resilience Analysis of Crisis in Medical Environments: A Structural Equation Modeling based on Crisis Management Components

International Journal of Occupational Hygiene ◽

10.18502/ijoh.v13i2.8367 ◽

2022 ◽

Author(s):

SAMIRA GHIYASI ◽

FATEMEH VERDI BAGHDADI ◽

FARSHAD HASHEMZADEH ◽

AHMAD SOLTANZADEH

Keyword(s):

Structural Equation Modeling ◽

Crisis Management ◽

Work Experience ◽

Structural Equation ◽

Goodness Of Fit ◽

Equation Modeling ◽

Fit Indices ◽

Cross Sectional ◽

Resilience Index ◽

The Impact

Enhancing the index of crisis resilience is one of the key goals in medical environments. Various parameters can affect crisis resilience. The current study was designed to analyze crisis resilience in medical environments based on the crisis management components. This cross-sectional and descriptive-analytical study was performed in 14 hospitals and medical centers, in 2020. A sample size of 343.5 was determined based on the Cochran's formula. We used a 44-item crisis management questionnaire of Azadian et al. to collect data. The components of this questionnaire included management commitment, error learning, culture learning, awareness, preparedness, flexibility, and transparency. The data was analyzed based on the structural equation modeling approach using IBM SPSS AMOS v. 23.0. The participants’ age and work experience mean were 37.78±8.14 and 8.22±4.47 years. The index of crisis resilience was equal to 2.96±0.87. The results showed that all components of crisis management had a significant relationship with this index (p <0.05). The highest and lowest impact on the resilience index were related to preparedness (E=0.88) and transparency (E=0.60). The goodness of fit indices of this model including RMSEA, CFI, NFI, and NNFI (TLI) was 2.86, 0.071, 0.965, 0.972, and 0.978. The index of crisis resilience in the medical environments was at a moderate level. Furthermore, the structural equation modeling findings indicated that the impact of each component of crisis management should be considered in prioritizing measures to increase the level of resilience.

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A note on the cutoff values of alternative fit indices to evaluate measurement invariance for ESEM models

International Journal of Behavioral Development ◽

10.1177/0165025419866911 ◽

2019 ◽

Vol 44 (2) ◽

pp. 166-174

Author(s):

Ying Jin

Keyword(s):

Measurement Invariance ◽

Structural Equation ◽

Mean Squared Error ◽

Simulated Data ◽

Index Formula ◽

Equation Modeling ◽

Approximation Formula ◽

Fit Indices ◽

Cutoff Values ◽

Partial Invariance

This research examines the performance of the previously proposed cutoff values of alternative fit indices (i.e., change in comparative fit index [[Formula: see text]], change in Tucker–Lewis index [[Formula: see text]], and change in root mean squared error of approximation [[Formula: see text]]) to evaluate measurement invariance for exploratory structural equation modeling (ESEM) models with simulated data. It is important to revisit these cutoff values because they were used widely in validity studies utilizing ESEM models to evaluate measurement invariance for ordinal indicators, but in fact, these cutoff values were developed under confirmatory factor analysis models with continuous indicators. Results of this study show that different cutoff values of [Formula: see text], [Formula: see text], and [Formula: see text] should be used for ESEM models with ordinal indicators. Evaluation of partial invariance for ESEM models is also discussed.

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Evaluation of Penman-Monteith Model Based on Sentinel-2 Data for the Estimation of Actual Evapotranspiration in Vineyards

Remote Sensing ◽

10.3390/rs13030478 ◽

2021 ◽

Vol 13 (3) ◽

pp. 478

Author(s):

Víctor García-Gutiérrez ◽

Claudio Stöckle ◽

Pilar Macarena Gil ◽

Francisco Javier Meza

Keyword(s):

Goodness Of Fit ◽

Mean Squared Error ◽

Estimation Method ◽

Actual Evapotranspiration ◽

Vitis Vinifera L ◽

Landsat 8 ◽

Temporal Scales ◽

Root Mean Squared Error ◽

Squared Error ◽

Sentinel 2

Water scarcity is one of the most important problems of agroecosystems in Mediterranean and semiarid areas, especially for species such as vineyards that largely depend on irrigation. Actual evapotranspiration (ET) is a variable that represents water consumption of a crop, integrating climate and biophysical variables. Actual evapotranspiration models based on remote sensing data from visible bands of Sentinel-2, including Penman-Monteith–Stewart (RS-PMS) and Penman-Monteith–Leuning (RS-PML), were evaluated at different temporal scales in a Cabernet Sauvignon vineyard (Vitis vinifera L.) located in central Chile, and their performance compared with independent ET measurements from an eddy covariance system (EC) and outputs from models based on thermal infrared data from Landsat 7 and Landsat 8, such as Mapping EvapoTranspiration with high Resolution and Internalized Calibration (METRIC) and Priestley–Taylor Two-Source Model (TSEB-PT). The RS-PMS model showed the best goodness of fit for all temporal scales evaluated, especially at instantaneous and daily ET, with root mean squared error (RMSE) of 28.9 Wm−2 and 0.52 mm day−1, respectively, and Willmott agreement index (d1) values of 0.77 at instantaneous scale and 0.7 at daily scale. Additionally, both approaches of RS-PM model were evaluated incorporating a soil evaporation estimation method, one considering the soil water content (fSWC) and the other hand, using the ratio of accumulated precipitation and equivalent evaporation (fZhang), achieving the best fit at instantaneous scale for RS-PMS fSWC method with relative root mean squared error (%RMSE) of 15.2% in comparison to 58.8% of fZhang. Finally, the relevance of the RS-PMS model was highlighted in the assessment and monitoring of vineyard drip irrigation in terms of crop coefficient (Kc) estimation, which is one of the methods commonly used in irrigation planning, yielding a comparable Kc to the one obtained by the EC tower with a bias around 9%.

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A Model on the Contribution of School Assets to the Achievement of Adolescents’ Well-Being and Academic Performance

The Spanish Journal of Psychology ◽

10.1017/sjp.2017.47 ◽

2017 ◽

Vol 20 ◽

Author(s):

Miguel-Ángel Pertegal ◽

Alfredo Oliva

Keyword(s):

Life Satisfaction ◽

Academic Performance ◽

Structural Equation ◽

Goodness Of Fit ◽

School Connectedness ◽

Well Being ◽

Self Report ◽

Equation Modeling ◽

Fit Indices ◽

Key Factor

AbstractThe aim of this study was to examine a model on the contribution of school assets on the development of adolescent´s well-being and school success. The sample comprised 1944 adolescents (893 girls and 1051 boys) aged between 12 and 17 years (M= 14.4;SD= 1.13), from secondary schools in Western Andalusia, which completed some self-report questionnaires. The results of structural equation modeling showed the goodness of fit of the initial theoretical model. This model confirmed the importance of school connectedness as a key factor in the relationships between other school assets (social climate; clarity of the rules and values, and positive opportunities and empowerment) and commitment to learning, academic performance and life satisfaction. However, the re-specification of the initial model considered two complementary paths with theoretical sense: first, a direct influence between clarity of the rules and values and commitment to learning, and second, between academic performance and life satisfaction. This model obtained better goodness of fit indices than the first one: χ2= 16.32;gl= 8;p= .038; χ2/gl= 2.04; SRMR = .018; RSMEA = .023 (95% C.I. = .005; 040); NNFI = .98; CFI = .99. From our study, the need to invest in initiatives focused on the promotion of adolescents’ links with their school emerges as a key goal to contribute towards, at the same time, both a good academic performance and a better life satisfaction.

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Effects of Social Identity, Self-Esteem, Schooling, and Age on Hope [Efectos de la Identidad Social, la autoestima, la Escolaridad y la Edad sobre la esperanza]

Acción Psicológica ◽

10.5944/ap.17.1.25221 ◽

2021 ◽

Vol 17 (1) ◽

pp. 61

Author(s):

Cirilo Humberto Garcia ◽

Leopoldo Daniel-González ◽

Adrián Valle de la O ◽

Héctor L. Diaz ◽

Laura K. Castro ◽

...

Keyword(s):

Social Identity ◽

Structural Equation ◽

Goodness Of Fit ◽

Explanatory Power ◽

Self Esteem ◽

Primary Objective ◽

Equation Modeling ◽

Fit Indices ◽

Explained Variance ◽

Probabilistic Sample

AbstractThe primary objective of this study was to analyze the direct explanatory power of social identity, schooling, and age on self-esteem, as well as the indirect effects of those variables (through the mediating variable self-esteem) on hope. A non-probabilistic sample composed of 657 persons from southern Nuevo Leon was recruited (mean age = 39.75 years; SD = 16.96). Structural equation modeling was used to analyze the effects, both direct and indirect, of the independent variables upon the dependent variables. With regard to hope, the model yields an explained variance of 37% (d ≥ 26% = large effect size) and shows well goodness-of-fit indices: χ2 / df = 2.618, GFI = .997, AFGI = .978, CFI = .995, NNFI = .995, NFI = .992, RMSEA = .048 (IC90%, .001, .100), and SRMR = .017. It is concluded that social identity, together with some contextual variables of a personal nature (for instance, age and schooling) is probably very important to explain the levels of self-esteem and hopeResumenEl objetivo primario de este estudio fue analizar el poder explicativo de las variables identidad social, escolaridad y edad, directamente sobre la autoestima y los efectos indirectos de las tres primeras, a través de la autoestima, sobre la esperanza. Se realizó el estudio en una muestra no probabilística de 657 hombres y mujeres, con edad promedio de 39.75 años (DE = 16.96). Se usó modelamiento de ecuaciones estructurales para analizar los efectos, tanto directos como indirectos, de las variables independientes sobre las dependientes. Se encuentra que el modelo tiene una varianza explicada del 37% (d = ≥ 26% = tamaño del efecto grande) en esperanza, con buenos indicadores de bondad de ajuste: χ2/gl = 2.618; GFI = .997; AFGI = .978; CFI = .995; NNFI = .995; NFI = .992; RMSEA = .048 (IC90%, .000, .100), SRMR = .017. Se concluye que probablemente la identidad social, junto con algunas variables contextuales de tipo personal, como la edad y la escolaridad, es prioritaria para explicar la existencia de la autoestima y de la esperanza.

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The Impact of the Learning Effectiveness on Alumni Employability: A Case Study of a T/I Department in Taiwan

Studies in English Language Teaching ◽

10.22158/selt.v4n4p586 ◽

2016 ◽

Vol 4 (4) ◽

pp. 586

Author(s):

Pin-Shan Hsiung

Keyword(s):

Structural Equation ◽

Goodness Of Fit ◽

Core Competency ◽

Equation Modeling ◽

Parameter Estimates ◽

Learning Effectiveness ◽

Fit Indices ◽

Academic Advancement ◽

Current Employment Status ◽

The Impact

In recent years, the number of translation and interpretation courses offered in Taiwan has increased rapidly, but few studies has looked at the employability of their graduates. This paper is aimed to investigate the direct effects of curriculum on the professional careers of alumni as reflected in their current employment status and level of academic advancement. A questionnaire survey was carried out to evaluate multiple aspects of teaching, including learning effectiveness, core competency, curriculum design and repay the society. Through an analysis of 150 named and 300 anonymous questionnaires, this study analyzed the learning effectiveness as the mediator for the careers of alumni, using the Amos statistical package for Structural Equation Modeling (SEM), along with other related techniques, such as Confirmatory Factor Analysis (CFA). The analyses have produced parameter estimates and goodness-of-fit indices, which could be useful for many purposes, such as examining longitudinal data and comparing groups. It is hoped that this brief study may provide a better understanding and a basis for future studies.

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