We briefly outline the information-theoretic (I-T) approaches to valid inference including a review of some simple methods for making formal inference from all the hypotheses in the model set (multimodel inference). The I-T approaches can replace the usual t tests and ANOVA tables that are so inferentially limited, but still commonly used. The I-T methods are easy to compute and understand and provide formal measures of the strength of evidence for both the null and alternative hypotheses, given the data. We give an example to highlight the importance of deriving alternative hypotheses and representing these as probability models. Fifteen technical issues are addressed to clarify various points that have appeared incorrectly in the recent literature. We offer several remarks regarding the future of empirical science and data analysis under an I-T framework.

/pdf/aic-model-selection-and-multimodel-inference-in-behavioral-192nrc36ut.pdf

Applications of Statistics

AIC model selection and multimodel inference in behavioral ecology: some background, observations, and comparisons

Box plots display batches of data. Five values from a set of data are conventionally used; the extremes, the upper and lower hinges (quartiles), and the median. Such plots are becoming a widely used tool in exploratory data analysis and in preparing visual summaries for statisticians and nonstatisticians alike. Three variants of the basic display, devised by the authors, are described. The first visually incorporates a measure of group size; the second incorporates an indication of rough significance of differences between medians; the third combines the features of the first two. These techniques are displayed by examples.

https://www.jstor.org/stable/pdfplus/2683468.pdf

Variations of Box Plots

Specification searches in covariance structure modeling

A multidimensional Rasch-type item response model, the multidimensional random coefficients multinomial logit model, is presented as an extension to the Adams & Wilson (1996) random coefficients multinomial logit model. The model is developed in a form that permits generalization to the multidimensional case of a wide class of Rasch models, including the simple logistic model, Masters' partial credit model, Wilson's ordered partition model, and Fischer's linear logistic model. Moreover, the model includes several existing multidimensional models as special cases, including Whitely's multicomponent latent trait model, Andersen's multidimensional Rasch model for repeated testing, and Embretson's multidimensional Rasch model for learning and change. Marginal maximum likelihood estimators for the model are derived and the estimation is examined using a simulation study. Implications and applications of the model are discussed and an example is given.

The Multidimensional Random Coefficients Multinomial Logit Model

http://levis.sggw.pl/~rew/scenes/pdf/Ozesmi.pdf

Applications of Statistics

Citations

AIC model selection and multimodel inference in behavioral ecology: some background, observations, and comparisons

Variations of Box Plots

Specification searches in covariance structure modeling

The Multidimensional Random Coefficients Multinomial Logit Model

Ecological models based on people’s knowledge: a multi-step fuzzy cognitive mapping approach

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