| Title:
|
Simulation studies on model search in $3$-dimensional contingency tables. Preliminary results (English) |
| Author:
|
Bismarck, Malte |
| Author:
|
Deutschmann, Christel |
| Author:
|
Králová, Dana |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1990 |
| Pages:
|
1-15 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
contingency table |
| Keyword:
|
model search |
| Keyword:
|
measures for decision |
| Keyword:
|
log-linear model |
| Keyword:
|
simulation study |
| Keyword:
|
log-linear models |
| Keyword:
|
3-dimensional contingency tables |
| Keyword:
|
empirical frequencies |
| MSC:
|
62E25 |
| MSC:
|
62H17 |
| MSC:
|
65C05 |
| idZBL:
|
Zbl 0698.62056 |
| idMR:
|
MR1039407 |
| DOI:
|
10.21136/AM.1990.104383 |
| . |
| Date available:
|
2008-05-20T18:38:12Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104383 |
| . |
| Reference:
|
[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. Zbl 0283.62006, MR 0483125 |
| Reference:
|
[2] H. Akaike: A new look at the statistical model identification.IEEE Transcations on Automatic Control AC-19 (1974), 716-723. Zbl 0314.62039, MR 0423716, 10.1109/TAC.1974.1100705 |
| Reference:
|
[3] H. Akaike J. Sakamoto: Analysis of cross-classified data by AIC.Ann. Inst. Statist. Math. 30 (1978), Part B, 185-197. MR 0507093 |
| Reference:
|
[4] Ch. Deutschmann: Fitting of models in multidimensional contingency table analysis as a biometrical problem.Dissertation A, Halle (1985). |
| Reference:
|
[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. 10.1080/00401706.1971.10488753 |
| Reference:
|
[6] L. A. Goodmann: A modified multiple regression approach to the analysis of dichotomous variables.American Sociological Review 37 (1972), 28-46. 10.2307/2093491 |
| Reference:
|
[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. 10.1080/01621459.1973.10481357 |
| Reference:
|
[8] N. Victor: Analysis of multidimensional contingency tables.Dissertation A, Mainz (1970). |
| Reference:
|
[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. 10.1037/0033-2909.93.1.149 |
| . |
