Cross-Classification Multilevel Logistic Models in Psychometrics

2003 ◽  
Vol 28 (4) ◽  
pp. 369-386 ◽  
Author(s):  
Wim Van den Noortgate ◽  
Paul De Boeck ◽  
Michel Meulders
Keyword(s):  
Random Sample ◽  
Multilevel Model ◽  
Multilevel Models ◽  
Population Distribution ◽  
Logistic Models ◽  
Educational Measurement ◽  
Random Parameters ◽  
Irt Models ◽  
Cross Classification ◽  
Item Effects

In IRT models, responses are explained on the basis of person and item effects. Person effects are usually defined as a random sample from a population distribution. Regular IRT models therefore can be formulated as multilevel models, including a within-person part and a between-person part. In a similar way, the effects of the items can be studied as random parameters, yielding multilevel models with a within-item part and a between-item part. The combination of a multilevel model with random person effects and one with random item effects leads to a cross-classification multilevel model, which can be of interest for IRT applications. The use of cross-classification multilevel logistic models will be illustrated with an educational measurement application.

Examining the Robustness of the Graded Response and 2-Parameter Logistic Models to Violations of Construct Normality

2022 ◽  
pp. 001316442110634
Author(s):  
Patrick D. Manapat ◽  
Michael C. Edwards
Keyword(s):  
Logistic Model ◽  
Population Distribution ◽  
Latent Trait ◽  
Logistic Models ◽  
Skewed Distribution ◽  
Parameter Recovery ◽  
Irt Models ◽  
Psychological Theories ◽  
Graded Response ◽  
Computationally Intensive

When fitting unidimensional item response theory (IRT) models, the population distribution of the latent trait (θ) is often assumed to be normally distributed. However, some psychological theories would suggest a nonnormal θ. For example, some clinical traits (e.g., alcoholism, depression) are believed to follow a positively skewed distribution where the construct is low for most people, medium for some, and high for few. Failure to account for nonnormality may compromise the validity of inferences and conclusions. Although corrections have been developed to account for nonnormality, these methods can be computationally intensive and have not yet been widely adopted. Previous research has recommended implementing nonnormality corrections when θ is not “approximately normal.” This research focused on examining how far θ can deviate from normal before the normality assumption becomes untenable. Specifically, our goal was to identify the type(s) and degree(s) of nonnormality that result in unacceptable parameter recovery for the graded response model (GRM) and 2-parameter logistic model (2PLM).

Assessing and Explaining Differential Item Functioning Using Logistic Mixed Models

2005 ◽  
Vol 30 (4) ◽  
pp. 443-464 ◽  
Author(s):  
Wim Van den Noortgate ◽  
Paul De Boeck
Keyword(s):  
Differential Item Functioning ◽  
Random Sample ◽  
Mixed Models ◽  
Mixed Model ◽  
Educational Measurement ◽  
Mixed Model Approach ◽  
Differential Functioning ◽  
Item Functioning ◽  
Item Effects ◽  
Model Approach

Although differential item functioning (DIF) theory traditionally focuses on the behavior of individual items in two (or a few) specific groups, in educational measurement contexts, it is often plausible to regard the set of items as a random sample from a broader category. This article presents logistic mixed models that can be used to model uniform DIF, treating the item effects and their interaction with groups (DIF) as random. In a similar way, the group effects can be modeled as random instead of fixed, if the groups can be considered a random sample from a population of groups. The models can, furthermore, be adapted easily for modeling DIF over individual persons rather than over groups, or for modeling the differential functioning of groups of items instead of individual items. It is shown that the logistic mixed model approach is not only a comprehensive and economical way to detect these different kinds of DIF, it also encourages us to explore possible explanations of DIF by including group or item covariates in the model.

Modeling Intraindividual Variability in Three-Level Multilevel Models

Methodology ◽  
2018 ◽  
Vol 14 (3) ◽  
pp. 95-108 ◽  
Author(s):  
Steffen Nestler ◽  
Katharina Geukes ◽  
Mitja D. Back
Keyword(s):  
Multilevel Model ◽  
Multilevel Models ◽  
Mixed Effects ◽  
Repeated Measurements ◽  
Scale Model ◽  
Suggested Approach ◽  
Psychological Study ◽  
Level Data ◽  
Ecological Momentary ◽  
Momentary Assessment

Abstract. The mixed-effects location scale model is an extension of a multilevel model for longitudinal data. It allows covariates to affect both the within-subject variance and the between-subject variance (i.e., the intercept variance) beyond their influence on the means. Typically, the model is applied to two-level data (e.g., the repeated measurements of persons), although researchers are often faced with three-level data (e.g., the repeated measurements of persons within specific situations). Here, we describe an extension of the two-level mixed-effects location scale model to such three-level data. Furthermore, we show how the suggested model can be estimated with Bayesian software, and we present the results of a small simulation study that was conducted to investigate the statistical properties of the suggested approach. Finally, we illustrate the approach by presenting an example from a psychological study that employed ecological momentary assessment.

scholarly journals Analysis of Factors Affecting the High Subjective Well-Being of Chinese Residents Based on the 2014 China Family Panel Study

2019 ◽  
Vol 16 (14) ◽  
pp. 2566 ◽  
Author(s):  
Wen Xu ◽  
Haiyan Sun ◽  
Bo Zhu ◽  
Wei Bai ◽  
Xiao Yu ◽  
...  
Keyword(s):  
Physical Exercise ◽  
Influencing Factors ◽  
Low Income ◽  
Social Trust ◽  
Population Distribution ◽  
Panel Study ◽  
Multivariable Analysis ◽  
Logistic Models ◽  
Well Being ◽  
Subjective Well Being

(1) Purpose: The purpose of our research is to understand the subjective well-being (SWB) of Chinese adult residents and its influencing factors and to identify the key groups and areas to provide a basis for the formulation of relevant policies to improve residents’ happiness. (2) Methods: In this study, we analyzed the influencing factors of SWB of individuals older than 16 years of age, according to the 2014 China Family Panel Study (CFPS). We weighted 27,706 samples in the database to achieve the purpose of representing the whole country. Finally, descriptive statistics were used for the population distribution, chi-square tests were used for univariable analysis, and binary logistic models were used for multivariable analysis. (3) Results: The response rate of SWB was 74.58%. Of the respondents, 71.2% had high SWB (7–10), with a U-shaped distribution between age and SWB. Females are more likely than males to rate themselves as happy. There is a positive ratio between years of education and SWB. Residents who have better self-evaluated income, self-rated health (SRH), psychological well-being (PWB), Body Mass Index (BMI), social trust, social relationships, and physical exercise have higher SWB. (4) Conclusion: The results of the present study indicate that to improve residents’ SWB, we should focus more attention on middle-aged and low-income groups, particularly men in agriculture. The promotion of SWB should be facilitated by improvements in residents’ education, health status, and social support as well as by the promotion of smoking bans and physical exercise.

scholarly journals Within-cluster resampling for multilevel models under informative cluster size

Biometrika ◽  
2019 ◽  
Vol 106 (4) ◽  
pp. 965-972
Author(s):  
D Lee ◽  
J K Kim ◽  
C J Skinner
Keyword(s):  
Maximum Likelihood ◽  
Cluster Size ◽  
Multilevel Model ◽  
Multilevel Models ◽  
Fixed Number ◽  
Regression Coefficients ◽  
Likelihood Estimator ◽  
Correct Model ◽  
Resampling Method ◽  
Informative Cluster Size

Summary A within-cluster resampling method is proposed for fitting a multilevel model in the presence of informative cluster size. Our method is based on the idea of removing the information in the cluster sizes by drawing bootstrap samples which contain a fixed number of observations from each cluster. We then estimate the parameters by maximizing an average, over the bootstrap samples, of a suitable composite loglikelihood. The consistency of the proposed estimator is shown and does not require that the correct model for cluster size is specified. We give an estimator of the covariance matrix of the proposed estimator, and a test for the noninformativeness of the cluster sizes. A simulation study shows, as in Neuhaus & McCulloch (2011), that the standard maximum likelihood estimator exhibits little bias for some regression coefficients. However, for those parameters which exhibit nonnegligible bias, the proposed method is successful in correcting for this bias.

scholarly journals On estimation in multilevel models with block circular symmetric covariance structure

2012 ◽  
Vol 16 (1) ◽  
pp. 83-96
Author(s):  
Yuli Liang ◽  
Dietrich von Rosen ◽  
Tatjana von Rosen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Parameter Space ◽  
Variance Components ◽  
Multilevel Model ◽  
Multilevel Models ◽  
Covariance Structure ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation

In this article we consider a multilevel model with block circular symmetric covariance structure. Maximum likelihood estimation of the parameters of this model is discussed. We show that explicit maximum likelihood estimators of variance components exist under certain restrictions on the parameter space.

scholarly journals The effects of misspecifying the random part of multilevel models

Methodology ◽  
2020 ◽  
Vol 16 (3) ◽  
pp. 224-240
Author(s):  
David M. LaHuis ◽  
Daniel R. Jenkins ◽  
Michael J. Hartman ◽  
Shotaro Hakoyama ◽  
Patrick C. Clark
Keyword(s):  
Effect Size ◽  
Fixed Effects ◽  
Multilevel Model ◽  
Multilevel Models ◽  
The Other ◽  
Standard Errors ◽  
Moderate Effect Size ◽  
Moderate Effect ◽  
Level 1 ◽  
Random Part

This paper examined the amount bias in standard errors for fixed effects when the random part of a multilevel model is misspecified. Study 1 examined the effects of misspecification for a model with one Level 1 predictor. Results indicated that misspecifying random slope variance as fixed had a moderate effect size on the standard errors of the fixed effects and had a greater effect than misspecifying fixed slopes as random. In Study 2, a second Level 1 predictor was added and allowed for the examination of the effects of misspecifying the slope variance of one predictor on the standard errors for the fixed effects of the other predictor. Results indicated that only the standard errors of coefficient relevant to that predictor were impacted and that the effect size for the bias could be considered moderate to large. These results suggest that researchers can use a piecemeal approach to testing multilevel models with random effects.

Multilevel Models

2009 ◽  
Author(s):  
Bradford S. Jones
Keyword(s):  
Random Effects ◽  
Data Structures ◽  
Multilevel Model ◽  
Multilevel Models ◽  
Great Promise ◽  
Hierarchical Data ◽  
Hierarchical Data Structures ◽  
Fixed And Random Effects

This article addresses multilevel models in which units are nested within one another. The focus is primarily two-level models. It also describes cross-unit heterogeneity. Moreover, it assesses the fixed and random effects from the multilevel model. It generally tries to convey the scope of multilevel models but in a very compact way. Multilevel models provide great promise for exploiting information in hierarchical data structures. There are a range of alternatives for such data and it bears repeating that sometimes, simpler-to-apply correctives are best.

Use OE Ranked Set Sampling for Test of a Normal Mean

1994 ◽  
Vol 44 (3-4) ◽  
pp. 183-194 ◽  
Author(s):  
Wei-Hsiung Shen
Keyword(s):  
Random Sample ◽  
Unbiased Estimator ◽  
Population Distribution ◽  
Simple Random Sample ◽  
Sample Mean ◽  
Ranked Set Sample ◽  
Normal Test ◽  
Normal Mean ◽  
Normal Variance ◽  
Better Than

In situations where the experimental or sampling units in a study can be easily ranked than quantified, Mcintyre (1952) proposed the notion of a ranked set sample ( RSS), and observed that, to estimate the population mean, the sample mean based on a RSS sample of size n provides an unbiased estimator with a smaller variance compared to a simple random sample mean of the same size n. Mcintyre's concept of RSS is essentially nonparametric in nature in that the underlying population distribution is assumed to be completely unknown. Sinha et al. (1992) in a recent paper further explored the concept of RSS and its many variations for estimation of a normal mean and a normal variance, and an exponential mean. In this paper we use the concept of RSS to derive tests for a normal mean μ when the variance is known, and show that many improved tests can be constructed, all of which are much better than the traditional normal test. All our tests are based on the improved eetimators of μ derived in Sinha et. al. (1992).

scholarly journals Differences in Rental and Nonrental Car Crashes

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Richard Tay ◽  
Jaisung Choi
Keyword(s):  
Rare Event ◽  
Logistic Models ◽  
Random Parameters ◽  
Related Factors ◽  
Risky Driving ◽  
Driving Behaviors ◽  
Random Parameters Logit ◽  
Car Crashes ◽  
Using Data ◽  
Risky Driving Behaviors

Although rental cars experience a higher collision rate per registered vehicle compared to nonrental cars, little research has been conducted to understand the differences in the factors contributing to crashes involving rental cars and nonrental cars, especially driver-related factors. This study develops a conceptual framework to compare the driver-related factors contributing to crashes involving rental cars and nonrental cars and tests the hypotheses developed using data from South Korea and applying the binary logistics, rare event logistics, Firth logistic models, and random parameters logit models. We found a significantly higher contribution of several risky driving behaviors but no differences in roadway, vehicle, and environmental factors. We also found that rental car crashes involve more males and drivers under 25 years of age.

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