Sensitivity of binomial N‐mixture models to overdispersion: The importance of assessing model fit

One of the greatest challenges in the application of finite mixture models is model comparison. A variety of statistical fit indices exist, including information criteria, approximate likelihood ratio tests, and resampling techniques; however, none of these indices describe the amount of improvement in model fit when a latent class is added to the model. We review these model fit statistics and propose a novel approach, the likelihood increment percentage per parameter (LIPpp), targeting the relative improvement in model fit when a class is added to the model. Simulation work based on two previous simulation studies highlighted the potential for the LIPpp to identify the correct number of classes, and provide context for the magnitude of improvement in model fit. We conclude with recommendations and future research directions.

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Is it appropriate to use fixed assay cut-offs for estimating seroprevalence?

Epidemiology and Infection ◽

10.1017/s0950268815001958 ◽

2015 ◽

Vol 144 (4) ◽

pp. 887-895 ◽

Cited By ~ 5

Author(s):

G. KAFATOS ◽

N. J. ANDREWS ◽

K. J. McCONWAY ◽

P. A. C. MAPLE ◽

K. BROWN ◽

...

Keyword(s):

Mixture Models ◽

Model Fit ◽

Alternative Methods ◽

Diagnostic Assay ◽

Past Infection ◽

Time Resolved ◽

Quantitative Measurements ◽

Good Distinction ◽

Susceptible Populations ◽

Biased Estimates

SUMMARYPopulation seroprevalence can be estimated from serosurveys by classifying quantitative measurements into positives (past infection/vaccinated) or negatives (susceptible) according to a fixed assay cut-off. The choice of assay cut-offs has a direct impact on seroprevalence estimates. A time-resolved fluorescence immunoassay (TRFIA) was used to test exposure to human parvovirus 4 (HP4). Seroprevalence estimates were obtained after applying the diagnostic assay cut-off under different scenarios using simulations. Alternative methods for estimating assay cut-offs were proposed based on mixture modelling with component distributions for the past infection/vaccinated and susceptible populations. Seroprevalence estimates were compared to those obtained directly from the data using mixture models. Simulation results showed that when there was good distinction between the underlying populations all methods gave seroprevalence estimates close to the true one. For high overlap between the underlying components, the diagnostic assay cut-off generally gave the most biased estimates. However, the mixture model methods also gave biased estimates which were a result of poor model fit. In conclusion, fixed cut-offs often produce biased estimates but they also have advantages compared to other methods such as mixture models. The bias can be reduced by using assay cut-offs estimated specifically for seroprevalence studies.

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Evidence for sponges as sister to all other animals from partitioned phylogenomics with mixture models and recoding

Nature Communications ◽

10.1038/s41467-021-22074-7 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Anthony K. Redmond ◽

Aoife McLysaght

Keyword(s):

Mixture Models ◽

Complex Traits ◽

Gradual Increase ◽

Sister Group ◽

Systematic Errors ◽

Model Fit ◽

Specific Level ◽

Origin And Evolution ◽

Simple Body ◽

Phylogenetic Models

AbstractResolving the relationships between the major lineages in the animal tree of life is necessary to understand the origin and evolution of key animal traits. Sponges, characterized by their simple body plan, were traditionally considered the sister group of all other animal lineages, implying a gradual increase in animal complexity from unicellularity to complex multicellularity. However, the availability of genomic data has sparked tremendous controversy as some phylogenomic studies support comb jellies taking this position, requiring secondary loss or independent origins of complex traits. Here we show that incorporating site-heterogeneous mixture models and recoding into partitioned phylogenomics alleviates systematic errors that hamper commonly-applied phylogenetic models. Testing on real datasets, we show a great improvement in model-fit that attenuates branching artefacts induced by systematic error. We reanalyse key datasets and show that partitioned phylogenomics does not support comb jellies as sister to other animals at either the supermatrix or partition-specific level.

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Finite Mixture Modeling for Program Evaluation: Resampling and Pre-processing Approaches

Evaluation Review ◽

10.1177/0193841x211065619 ◽

2021 ◽

pp. 0193841X2110656

Author(s):

Zachary K. Collier ◽

Haobai Zhang ◽

Bridgette Johnson

Keyword(s):

Mixture Models ◽

Finite Mixture Models ◽

Mixture Modeling ◽

Finite Mixture ◽

Model Fit ◽

Finite Mixture Modeling ◽

Resampling Methods ◽

Fit Statistics ◽

Latent Subgroups ◽

Nationally Representative

Background Finite mixture models cluster individuals into latent subgroups based on observed traits. However, inaccurate enumeration of clusters can have lasting implications on policy decisions and allocations of resources. Applied and methodological researchers accept no obvious best model fit statistic, and different measures could suggest different numbers of latent clusters. Objectives The purpose of this article is to evaluate and compare different cluster enumeration techniques. Research Design Study I demonstrates how recently proposed resampling methods result in no precise number of clusters on which all fit statistics agree. We recommend the pre-processing method in Study II as an alternative. Both studies used nationally representative data on working memory, cognitive flexibility, and inhibitory control. Conclusions The data plus priors method shows promise to address inconsistencies among fit measures and help applied researchers using finite mixture models in the future.

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Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

Swiss Journal of Psychology ◽

10.1024/1421-0185.67.1.51 ◽

2008 ◽

Vol 67 (1) ◽

pp. 51-60 ◽

Cited By ~ 26

Author(s):

Stefano Passini

Keyword(s):

Social Dominance ◽

Factor Model ◽

Three Dimensional ◽

Social Dominance Orientation ◽

Model Fit ◽

Regression Analyses ◽

One Dimensional ◽

Confirmatory Factor ◽

The One ◽

Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

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Following the Ants

European Journal of Psychological Assessment ◽

10.1027/1015-5759/a000299 ◽

2017 ◽

Vol 33 (6) ◽

pp. 409-421 ◽

Cited By ~ 10

Author(s):

Anne B. Janssen ◽

Martin Schultze ◽

Adrian Grötsch

Keyword(s):

Short Form ◽

Supervisor Support ◽

Proactive Personality ◽

Work Behavior ◽

Model Fit ◽

Item Selection ◽

Short Version ◽

Innovative Work Behavior ◽

Innovative Work ◽

Two Measures

Abstract. Employees’ innovative work is a facet of proactive work behavior that is of increasing interest to industrial and organizational psychologists. As proactive personality and supervisor support are key predictors of innovative work behavior, reliable, and valid employee ratings of these two constructs are crucial for organizations’ planning of personnel development measures. However, the time for assessments is often limited. The present study therefore aimed at constructing reliable short scales of two measures of proactive personality and supervisor support. For this purpose, we compared an innovative approach of item selection, namely Ant Colony Optimization (ACO; Leite, Huang, & Marcoulides, 2008 ) and classical item selection procedures. For proactive personality, the two item selection approaches provided similar results. Both five-item short forms showed a satisfactory reliability and a small, however negligible loss of criterion validity. For a two-dimensional supervisor support scale, ACO found a reliable and valid short form. Psychometric properties of the short version were in accordance with those of the parent form. A manual supervisor support short form revealed a rather poor model fit and a serious loss of validity. We discuss benefits and shortcomings of ACO compared to classical item selection approaches and recommendations for the application of ACO.

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From Bi-Dimensionality to Uni-Dimensionality in Self-Report Questionnaires

European Journal of Psychological Assessment ◽

10.1027/1015-5759/a000583 ◽

2020 ◽

pp. 1-14 ◽

Cited By ~ 1

Author(s):

Bjarne Schmalbach ◽

Markus Zenger ◽

Michalis P. Michaelides ◽

Karin Schermelleh-Engel ◽

Andreas Hinz ◽

...

Keyword(s):

Factor Model ◽

Common Factor ◽

Self Regulation ◽

Model Fit ◽

Self Report ◽

External Criterion ◽

Common Factor Model ◽

Random Intercept ◽

Using Data ◽

Core Self

Abstract. The common factor model – by far the most widely used model for factor analysis – assumes equal item intercepts across respondents. Due to idiosyncratic ways of understanding and answering items of a questionnaire, this assumption is often violated, leading to an underestimation of model fit. Maydeu-Olivares and Coffman (2006) suggested the introduction of a random intercept into the model to address this concern. The present study applies this method to six established instruments (measuring depression, procrastination, optimism, self-esteem, core self-evaluations, and self-regulation) with ambiguous factor structures, using data from representative general population samples. In testing and comparing three alternative factor models (one-factor model, two-factor model, and one-factor model with a random intercept) and analyzing differential correlational patterns with an external criterion, we empirically demonstrate the random intercept model’s merit, and clarify the factor structure for the above-mentioned questionnaires. In sum, we recommend the random intercept model for cases in which acquiescence is suspected to affect response behavior.

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Mindfulness or Mindlessness?

European Journal of Psychological Assessment ◽

10.1027/1015-5759/a000045 ◽

2011 ◽

Vol 27 (1) ◽

pp. 59-64 ◽

Cited By ~ 25

Author(s):

Volkmar Höfling ◽

Helfried Moosbrugger ◽

Karin Schermelleh-Engel ◽

Thomas Heidenreich

Keyword(s):

Construct Validity ◽

Model Fit ◽

Factor Analyses ◽

Confirmatory Factor Analyses ◽

Mindful Attention ◽

Confirmatory Factor ◽

Item Wording ◽

Method Effects

The 15 items of the Mindful Attention and Awareness Scale (MAAS; Brown & Ryan, 2003 ) are negatively worded and assumed to assess mindfulness. However, there are indications of differences between the original MAAS and a version with the positively rephrased MAAS items (“mirror items”). The present study examines whether the mindfulness facet “mindful attention and awareness” (MAA) can be measured with both positively and negatively worded items if we take method effects due to item wording into account. To this end, the 15 negatively worded items of the MAAS and additionally 13 positively rephrased items were assessed (N = 602). Confirmatory factor analyses (CFA) models with and without regard to method effects were carried out and evaluated by means of model fit. As a result, the positively and negatively worded items should be seen as different methods that influence the construct validity of mindfulness. Furthermore, a modified version of the MAAS (MAAS-Short) with five negatively worded items (taken from the MAAS) and five positively worded items (“mirror items”) was introduced as an alternative to assess MAA. The MAAS-Short appears superior to the original MAAS. The results and the limitations of the present study are discussed.

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Factorial Structure of the Therapist Adherence Measure-Revised (TAM-R) Within Multisystemic Therapy

European Journal of Psychological Assessment ◽

10.1027/1015-5759/a000505 ◽

2020 ◽

Vol 36 (2) ◽

pp. 427-431

Author(s):

Aurelie M. C. Lange ◽

Marc J. M. H. Delsing ◽

Ron H. J. Scholte ◽

Rachel E. A. van der Rijken

Keyword(s):

Factor Analysis ◽

Factor Structure ◽

Factor Model ◽

Multisystemic Therapy ◽

Model Fit ◽

Validity And Reliability ◽

Adherence Measure ◽

Therapist Adherence ◽

Confirmatory Factor ◽

The Us

Abstract. The Therapist Adherence Measure (TAM-R) is a central assessment within the quality-assurance system of Multisystemic Therapy (MST). Studies into the validity and reliability of the TAM in the US have found varying numbers of latent factors. The current study aimed to reexamine its factor structure using two independent samples of families participating in MST in the Netherlands. The factor structure was explored using an Exploratory Factor Analysis (EFA) in Sample 1 ( N = 580). This resulted in a two-factor solution. The factors were labeled “therapist adherence” and “client–therapist alliance.” Four cross-loading items were dropped. Reliability of the resulting factors was good. This two-factor model showed good model fit in a subsequent Confirmatory Factor Analysis (CFA) in Sample 2 ( N = 723). The current finding of an alliance component corroborates previous studies and fits with the focus of the MST treatment model on creating engagement.

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

Methodology ◽

10.1027/1614-2241/a000033 ◽

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.

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