| 1. |
- Gärdenfors, Peter, et al.
(author)
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Decision making with unreliable probabilities
- 1983
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In: British Journal of Mathematical & Statistical Psychology. - : Wiley. - 0007-1102. ; 36:2, s. 240-251
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Journal article (peer-reviewed)abstract
- This paper presents a decision theory which allows subjects to account for the uncertainties of their probability estimates. This is accomplished by modelling beliefs about states of nature by means of a class of probability measures. In order to represent uncertainties of those beliefs a measure of epistemic reliability is introduced. The suggested decision theory is evaluated in the light of empirical evidence on ambiguity and uncertainty in decision making. The theory is also compared to Tversky & Kahneman's prospect theory.
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| 2. |
- Jin, Shaobo, et al.
(author)
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Asymptotic Efficiency of the Pseudo-Maximum Likelihood Estimator in Multi-Group Factor Models with Pooled Data
- 2016
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In: British Journal of Mathematical & Statistical Psychology. - : Wiley. - 0007-1102 .- 2044-8317. ; 69:1, s. 20-42
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Journal article (peer-reviewed)abstract
- A multi-group factor model is suitable for data originating from different strata. However, it often requires a relatively large sample size to avoid numerical issues such as non-convergence and non-positive definite covariance matrices. An alternative is to pool data from different groups in which a single-group factor model is fitted to the pooled data using maximum likelihood. In this paper, properties of pseudo-maximum likelihood (PML) estimators for pooled data are studied. The pooled data are assumed to be normally distributed from a single group. The resulting asymptotic efficiency of the PML estimators of factor loadings is compared with that of the multi-group maximum likelihood estimators. The effect of pooling is investigated through a two-group factor model. The variances of factor loadings for the pooled data are underestimated under the normal theory when error variances in the smaller group are larger. Underestimation is due to dependence between the pooled factors and pooled error terms. Small-sample properties of the PML estimators are also investigated using a Monte Carlo study.
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| 3. |
- Jin, Shaobo, 1987-, et al.
(author)
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Selecting polychoric instrumental variables in confirmatory factor analysis : An alternative specification test and effects of instrumental variables
- 2018
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In: British Journal of Mathematical & Statistical Psychology. - : John Wiley & Sons. - 0007-1102 .- 2044-8317. ; 71:2, s. 387-413
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Journal article (peer-reviewed)abstract
- The polychoric instrumental variable (PIV) approach is a recently proposed method to fit a confirmatory factor analysis model with ordinal data. In this paper, we first examine the small‐sample properties of the specification tests for testing the validity of instrumental variables (IVs). Second, we investigate the effects of using different numbers of IVs. Our results show that specification tests derived for continuous data are extremely oversized at all sample sizes when applied to ordinal variables. Possible modifications for ordinal data are proposed in the present study. Simulation results show that the modified specification tests with all available IVs are able to detect model misspecification. In terms of estimation accuracy, the PIV approach where the IVs outnumber the endogenous variables by one produces a lower bias but a higher variation than the PIV approach with more IVs for correctly specified factor loadings at small samples.
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| 4. |
- Lantz, Björn
(author)
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The impact of sample non-normality on ANOVA and alternative methods
- 2013
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In: British Journal of Mathematical & Statistical Psychology. - : John Wiley & Sons Ltd.. - 0007-1102 .- 2044-8317. ; 66:2, s. 224-244
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Journal article (peer-reviewed)abstract
- In this journal, Zimmerman (2004, 2011) has discussed preliminary tests that researchers often use to choose an appropriate method for comparing locations when the assumption of normality is doubtful. The conceptual problem with this approach is that such a two-stage process makes both the power and the significance of the entire procedure uncertain, as type I and type II errors are possible at both stages. A type I error at the first stage, for example, will obviously increase the probability of a type II error at the second stage. Based on the idea of Schmider et al. (2010), which proposes that simulated sets of sample data be ranked with respect to their degree of normality, this paper investigates the relationship between population non-normality and sample non-normality with respect to the performance of the ANOVA, Brown–Forsythe test, Welch test, and Kruskal–Wallis test when used with different distributions, sample sizes, and effect sizes. The overall conclusion is that the Kruskal–Wallis test is considerably less sensitive to the degree of sample normality when populations are distinctly non-normal and should therefore be the primary tool used to compare locations when it is known that populations are not at least approximately normal.
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| 5. |
- Sahlin, Nils-Eric
(author)
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Preference among preferences as a method for obtaining a higher ordered metric scale
- 1981
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In: British Journal of Mathematical & Statistical Psychology. - : Wiley. - 0007-1102. ; 34:1, s. 62-75
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Journal article (peer-reviewed)abstract
- A method is presented for collecting data which yield a scale on which the entities are ranked in preference and all combinations of value distances are ranked (higher-ordered metric scale). The method is based on the concept of secondary preference, i.e. preference among preferences. This method is compared with a classical method based on 50–50 game comparison. Two empirical studies are presented. The first examines whether both methods yield the same ordering of value distances. The second involves empirical derivation of a higher-ordered metric scale.
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