Article
Full entry |
PDF
(2.5 MB)
Feedback
PDF
(2.5 MB)
Feedback
Keywords:
contingency table; model search; measures for decision; log-linear model; simulation study; log-linear models; 3-dimensional contingency tables; empirical frequencies
contingency table; model search; measures for decision; log-linear model; simulation study; log-linear models; 3-dimensional contingency tables; empirical frequencies
Summary:
In model search procedures for multidimensional contingency tables many different measures are used for decision for the goodness of model search, for instance $\alpha$, AIC or $R^2$. Simulation studies should give us an insight into the behaviour of the measures with respect to the data, the sample size, the number of degrees of freedom and the probability given distribution. To this end different log-linear models for 3-dimensional contingency tables were given and then 1,000 contingency tables were simulated for each model and for several sample sizes and the various decision measures were computed. Summarizing the results we count empirical frequencies of the choice of the true model under various circumstances. This leads to our concluding discussion of properties of the model acceptance criteria under consideration.
References:
[1] H. Akaike: Information theory and an extension of the maximum likelihood principle. 2nd International Symposium on Information Theory, B. N. Petrov and F. Csaki, Eds., Akademiai Kiado, Budapest (1973), 267-281. MR 0483125 | Zbl 0283.62006
[2] H. Akaike: A new look at the statistical model identification. IEEE Transcations on Automatic Control AC-19 (1974), 716-723. DOI 10.1109/TAC.1974.1100705 | MR 0423716 | Zbl 0314.62039
[3] H. Akaike J. Sakamoto: Analysis of cross-classified data by AIC. Ann. Inst. Statist. Math. 30 (1978), Part B, 185-197. MR 0507093
[4] Ch. Deutschmann: Fitting of models in multidimensional contingency table analysis as a biometrical problem. Dissertation A, Halle (1985).
[5] L. A. Goodman: The analysis of multidimensional contingency tables: stepwise procedure and discrete estimation methods for building models for multiple classifications. Technometrics 13, (197Ib), 33-61. DOI 10.1080/00401706.1971.10488753
[6] L. A. Goodmann: A modified multiple regression approach to the analysis of dichotomous variables. American Sociological Review 37 (1972), 28-46. DOI 10.2307/2093491
[7] L. A. Goodman: Guided and unguided methods for the selection of models for a set of T multidimensional contingency tables. J. Amer. Statist. Ass. 68 (1973), 165-175. DOI 10.1080/01621459.1973.10481357
[8] N. Victor: Analysis of multidimensional contingency tables. Dissertation A, Mainz (1970).
[9] Bonett G. Douglas P. M. Bentler: Goodness -of- Fit Procedures for the Evaluation and Selection of Log-Linear Models. Psychological Bulletin 93 (1983), 149-166. DOI 10.1037/0033-2909.93.1.149
Search
Partner of
