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Visualizing parameters from loglinear models

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Summary

This paper presents a graphical display for the parameters resulting from loglinear models. Loglinear models provide a method for analyzing associations between two or several categorical variables and have become widely accepted as a tool for researchers during the last two decades. An important part of the output of any computer program focused on loglinear models is that devoted to estimation of parameters in the model. Traditionally, this output has been presented using tables that indicate the values of the coefficients, the associated standard errors and other related information. Evaluation of these tables can be rather tedious because of the number of values shown as well as their rather complicated structure, mainly when the analyst needs to consider several models before reaching a model with a good fit. Therefore, a graphical display summarizing tables of parameters could be of great help in this situation. In this paper we put forward an interactive dynamic graphical display that could be used in such fashion.

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Acknowledgements

We are grateful for the comments of three anonymous reviewers for their helpful suggestions, which greatly improved this work.

This research was supported by Grants BSO2001-2904 and BSO2002-02513 from the Spanish Ministry of Science and Technology

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Annex A. Spreadplot for the model [AD, GD, AGD|D=A]

Description of the panes of the spreadplot for loglinear analysis (excluding the plot of parameters).

  1. (1)

    The list of terms: The list of terms allows for selection of the terms in the model. All possibilities are listed in this window. The user selects or deselects those required for a model by using Ctrl-mouse_click or Ctrlmousedrag. This list has two working modes. When the list is in the hierarchical mode, including an interaction term involves automatically adding all the terms hierarchically below the (added) one. On the other hand, when the list is in the non-hierarchical mode, each term is added or removed individually. Note that LoginViSta uses the same computational method for the fitting of hierarchical or non-hierarchical models (Tierney, 1991).

  2. (2)

    The Leverages versus the Cook distances plot: Friendly (2000) discusses scatterplots of residuals versus leverages for diagnosing loglinear models, adding the Cook distances as bubbles associated with each point. The plots here shown uses linking to display this information in two separate plots.

  3. (3)

    The Mosaic plots: The version of mosaic plots here shown is part of ViSta. It uses colors to display adjusted χ2 residuals and admits up to four variables. As cells with very low frequency are difficult to identify, LoginViSta permits plotting the square root of the values. LoginViSta plots a scatterplot of the raw frequencies versus the residuals when the data analyzed includes more than four variables.

  4. (4)

    The plot for fitted models: This plot keeps track of the χ2 divided by the degrees of freedom of the different models fitted during a session. Models below the horizontal line would pass the criteria of χ2/df < 1. Selecting a point in this plot changes the spreadplot to show the values for the model selected, including the list of terms. This makes it easy to return to past successful models when the currently tested one is inadequate. Also, this plot allows the testing of differences between nested models. When the user selects two points in the plot, the software will check if the models are nested and will then print the test if they are. Also, the mosaic plots will show the observed v. residual plots for both models.

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Valero-Mora, P., Rodrigo, M.F. & Young, F.W. Visualizing parameters from loglinear models. Computational Statistics 19, 113–135 (2004). https://doi.org/10.1007/BF02915279

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