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- Kraus, Katrin, 1979-
(författare)
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On the Measurement of Model Fit for Sparse Categorical Data
- 2012
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of four papers that deal with several aspects of the measurement of model fit for categorical data. In all papers, special attention is paid to situations with sparse data.The first paper concerns the computational burden of calculating Pearson's goodness-of-fit statistic for situations where many response patterns have observed frequencies that equal zero. A simple solution is presented that allows for the computation of the total value of Pearson's goodness-of-fit statistic when the expected frequencies of response patterns with observed frequencies of zero are unknown.In the second paper, a new fit statistic is presented that is a modification of Pearson's statistic but that is not adversely affected by response patterns with very small expected frequencies. It is shown that the new statistic is asymptotically equivalent to Pearson's goodness-of-fit statistic and hence, asymptotically chi-square distributed.In the third paper, comprehensive simulation studies are conducted that compare seven asymptotically equivalent fit statistics, including the new statistic. Situations that are considered concern both multinomial sampling and factor analysis. Tests for the goodness-of-fit are conducted by means of the asymptotic and the bootstrap approach both under the null hypothesis and when there is a certain degree of misfit in the data. Results indicate that recommendations on the use of a fit statistic can be dependent on the investigated situation and on the purpose of the model test. Power varies substantially between the fit statistics and the cause of the misfit of the model. Findings indicate further that the new statistic proposed in this thesis shows rather stable results and compared to the other fit statistics, no disadvantageous characteristics of the fit statistic are found.Finally, in the fourth paper, the potential necessity of determining the goodness-of-fit by two sided model testing is adverted. A simulation study is conducted that investigates differences between the one sided and the two sided approach of model testing. Situations are identified for which two sided model testing has advantages over the one sided approach.
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| 2. |
- Persson, Inger, et al.
(författare)
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Confirming the Structure of the Survey of Attitudes Toward Statistics (SATS-36) by Swedish Students
- 2019
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Ingår i: Statistics Education Research Journal. - : International Association for Statistical Education. - 1570-1824. ; 18:1, s. 83-93
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Tidskriftsartikel (refereegranskat)abstract
- Research on students’ attitudes toward statistics has attracted many statistics instructors and statistics education researchers. In this study, we use confirmatory factor analysis to analyze data collected from an introductory statistics course using the Survey of Attitudes toward Statistics. Theresults suggest that the items and six factors are conceptually relevant, confirming the six-factor structure of the pretest version of SATS-36 on this sample of Swedish students, with a few suggested modifications of the original model structure. Two items are excluded from the Difficulty component, two items on the Affect component are allowed to correlate, and two items on the Cognitive competence component are also allowed to correlate.
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| 3. |
- Pohl, Steffi, et al.
(författare)
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Modelling method effects as individual causal effects
- 2008
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Ingår i: Journal of the Royal Statistical Society. - 0964-1998 .- 1467-985X. ; 171:1, s. 41-63
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Tidskriftsartikel (refereegranskat)abstract
- Method effects often occur when different methods are used for measuring the same construct. We present a new approach for modelling this kind of phenomenon, consisting of a definition of method effects and a first model, the method effect model, that can be used for data analysis. This model may be applied to multitrait-multimethod data or to longitudinal data where the same construct is measured with at least two methods at all occasions. In this new approach, the definition of the method effects is based on the theory of individual causal effects by Neyman and Rubin. Method effects are accordingly conceptualized as the individual effects of applying measurement method j instead of k. They are modelled as latent difference scores in structural equation models. A reference method needs to be chosen against which all other methods are compared. The model fit is invariant to the choice of the reference method. The model allows the estimation of the average of the individual method effects, their variance, their correlation with the traits (and other latent variables) and the correlation of different method effects among each other. Furthermore, since the definition of the method effects is in line with the theory of causality, the method effects may (under certain conditions) be interpreted as causal effects of the method. The method effect model is compared with traditional multitrait-multimethod models. An example illustrates the application of the model to longitudinal data analysing the effect of negatively (such as 'feel bad') as compared with positively formulated items (such as 'feel good') measuring mood states.
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