Construction of informative priors for the application of CFA-MTMM models in small samples

When Bayesian estimation is used to analyze Structural Equation Models (SEMs), prior distributions need to be specified for all parameters in the model. Many popular software programs offer default prior distributions, which is helpful for novel users and makes Bayesian SEM accessible for a broad audience. However, when the sample size is small, those prior distributions are not always suitable and can lead to untrustworthy results. In this tutorial, we provide a non-technical discussion of the risks associated with the use of default priors in small sample contexts. We discuss how default priors can unintentionally behave as highly informative priors when samples are small. Also, we demonstrate an online educational Shiny app, in which users can explore the impact of varying prior distributions and sample sizes on model results. We discuss how the Shiny app can be used in teaching; provide a reading list with literature on how to specify suitable prior distributions; and discuss guidelines on how to recognize (mis)behaving priors. It is our hope that this tutorial helps to spread awareness of the importance of specifying suitable priors when Bayesian SEM is used with small samples.

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Applying the Anderson-Darling Test to Suicide Clusters

Crisis ◽

10.1027/0227-5910/a000197 ◽

2013 ◽

Vol 34 (6) ◽

pp. 434-437 ◽

Cited By ~ 5

Author(s):

Donald W. MacKenzie

Keyword(s):

Poisson Process ◽

Goodness Of Fit ◽

Small Samples ◽

Massachusetts Institute Of Technology ◽

Homogeneous Poisson Process ◽

Cornell University ◽

The Difference ◽

Suicide Clusters ◽

Institute Of Technology ◽

Anderson Darling

Background: Suicide clusters at Cornell University and the Massachusetts Institute of Technology (MIT) prompted popular and expert speculation of suicide contagion. However, some clustering is to be expected in any random process. Aim: This work tested whether suicide clusters at these two universities differed significantly from those expected under a homogeneous Poisson process, in which suicides occur randomly and independently of one another. Method: Suicide dates were collected for MIT and Cornell for 1990–2012. The Anderson-Darling statistic was used to test the goodness-of-fit of the intervals between suicides to distribution expected under the Poisson process. Results: Suicides at MIT were consistent with the homogeneous Poisson process, while those at Cornell showed clustering inconsistent with such a process (p = .05). Conclusions: The Anderson-Darling test provides a statistically powerful means to identify suicide clustering in small samples. Practitioners can use this method to test for clustering in relevant communities. The difference in clustering behavior between the two institutions suggests that more institutions should be studied to determine the prevalence of suicide clustering in universities and its causes.

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The German Version of the Satisfaction With Life Scale (SWLS)

European Journal of Psychological Assessment ◽

10.1027/1015-5759/a000058 ◽

2011 ◽

Vol 27 (2) ◽

pp. 127-132 ◽

Cited By ~ 180

Author(s):

Heide Glaesmer ◽

Gesine Grande ◽

Elmar Braehler ◽

Marcus Roth

Keyword(s):

Convergent Validity ◽

Satisfaction With Life ◽

Age Groups ◽

Population Based ◽

Factorial Invariance ◽

Satisfaction With Life Scale ◽

Small Samples ◽

Cross Sectional ◽

Confirmatory Factor Analyses ◽

Life Scale

The Satisfaction with Life Scale (SWLS) is the most commonly used measure for life satisfaction. Although there are numerous studies confirming factorial validity, most studies on dimensionality are based on small samples. A controversial debate continues on the factorial invariance across different subgroups. The present study aimed to test psychometric properties, factorial structure, factorial invariance across age and gender, and to deliver population-based norms for the German general population from a large cross-sectional sample of 2519 subjects. Confirmatory factor analyses supported that the scale is one-factorial, even though indications of inhomogeneity of the scale have been detected. Both findings show invariance across the seven age groups and both genders. As indicators of the convergent validity, a positive correlation with social support and negative correlation with depressiveness was shown. Population-based norms are provided to support the application in the context of individual diagnostics.

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Assessing Person Fit With the Information Matrix Test

Methodology ◽

10.1027/1614-2241/a000085 ◽

2015 ◽

Vol 11 (1) ◽

pp. 3-12 ◽

Cited By ~ 2

Author(s):

Jochen Ranger ◽

Jörg-Tobias Kuhn

Keyword(s):

Simulation Study ◽

Type I Error ◽

Information Matrix ◽

Small Samples ◽

Type I ◽

Person Fit ◽

Power Of The Test ◽

Order Expansion ◽

Trait Stability ◽

Information Matrix Test

In this manuscript, a new approach to the analysis of person fit is presented that is based on the information matrix test of White (1982) . This test can be interpreted as a test of trait stability during the measurement situation. The test follows approximately a χ2-distribution. In small samples, the approximation can be improved by a higher-order expansion. The performance of the test is explored in a simulation study. This simulation study suggests that the test adheres to the nominal Type-I error rate well, although it tends to be conservative in very short scales. The power of the test is compared to the power of four alternative tests of person fit. This comparison corroborates that the power of the information matrix test is similar to the power of the alternative tests. Advantages and areas of application of the information matrix test are discussed.

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