Simulation studies on model search in 3 -dimensional contingency tables. Preliminary results

Malte Bismarck; Christel Deutschmann; Dana Králová

Aplikace matematiky (1990)

  • Volume: 35, Issue: 1, page 1-15
  • ISSN: 0862-7940

Abstract

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In model search procedures for multidimensional contingency tables many different measures are used for decision for the goodness of model search, for instance α , 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.

How to cite

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Bismarck, Malte, Deutschmann, Christel, and Králová, Dana. "Simulation studies on model search in $3$-dimensional contingency tables. Preliminary results." Aplikace matematiky 35.1 (1990): 1-15. <http://eudml.org/doc/15606>.

@article{Bismarck1990,
abstract = {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.},
author = {Bismarck, Malte, Deutschmann, Christel, Králová, Dana},
journal = {Aplikace matematiky},
keywords = {contingency table; model search; measures for decision; log-linear model; simulation study; log-linear models; 3-dimensional contingency tables; empirical frequencies; model search; log-linear models; 3-dimensional contingency tables; decision measures; empirical frequencies},
language = {eng},
number = {1},
pages = {1-15},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Simulation studies on model search in $3$-dimensional contingency tables. Preliminary results},
url = {http://eudml.org/doc/15606},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Bismarck, Malte
AU - Deutschmann, Christel
AU - Králová, Dana
TI - Simulation studies on model search in $3$-dimensional contingency tables. Preliminary results
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 1
SP - 1
EP - 15
AB - 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.
LA - eng
KW - contingency table; model search; measures for decision; log-linear model; simulation study; log-linear models; 3-dimensional contingency tables; empirical frequencies; model search; log-linear models; 3-dimensional contingency tables; decision measures; empirical frequencies
UR - http://eudml.org/doc/15606
ER -

References

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  2. H. Akaike, 10.1109/TAC.1974.1100705, IEEE Transcations on Automatic Control AC-19 (1974), 716-723. (1974) Zbl0314.62039MR0423716DOI10.1109/TAC.1974.1100705
  3. H. Akaike J. Sakamoto, Analysis of cross-classified data by AIC, Ann. Inst. Statist. Math. 30 (1978), Part B, 185-197. (1978) Zbl0443.62040MR0507093
  4. Ch. Deutschmann, Fitting of models in multidimensional contingency table analysis as a biometrical problem, Dissertation A, Halle (1985). (1985) 
  5. L. A. Goodman, 10.1080/00401706.1971.10488753, Technometrics 13, (197Ib), 33-61. (197I) Zbl0218.62066DOI10.1080/00401706.1971.10488753
  6. L. A. Goodmann, 10.2307/2093491, American Sociological Review 37 (1972), 28-46. (1972) DOI10.2307/2093491
  7. L. A. Goodman, 10.1080/01621459.1973.10481357, J. Amer. Statist. Ass. 68 (1973), 165-175. (1973) DOI10.1080/01621459.1973.10481357
  8. N. Victor, Analysis of multidimensional contingency tables, Dissertation A, Mainz (1970). (1970) 
  9. Bonett G. Douglas P. M. Bentler, 10.1037/0033-2909.93.1.149, Psychological Bulletin 93 (1983), 149-166. (1983) DOI10.1037/0033-2909.93.1.149

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