A goodness-of-fit test for multinomial logistic regression. (English) Zbl 1116.62051
Summary: This article presents a score test to check the fit of a logistic regression model with two or more outcome categories. The null hypothesis that the model fits well is tested against the alternative that residuals of samples close to each other in the covariate space tend to deviate from the model in the same direction. We propose a test statistic that is a sum of squared smoothed residuals, and show that it can be interpreted as a score test in a random effects model. By specifying the distance metric in covariate space, users can choose the alternative against which the test is directed, making it either an omnibus goodness-of-fit test or a test for lack of fit of specific model variables or outcome categories.
MSC:
| 62G10 | Nonparametric hypothesis testing |
| 62J12 | Generalized linear models (logistic models) |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
Keywords:
liver enzyme data; polytomous logistic regression; discrete choice model; random effects model; smoothingReferences:
| [1] | Albert, Multivariate Interpretation of Clinical Laboratory Data (1987) |
| [2] | Cox, Theoretical Statistics (1974) · doi:10.1007/978-1-4899-2887-0 |
| [3] | Dudoit, Multiple hypothesis testing in microarray experiments, Statistical Science 18 pp 71– (2003) · Zbl 1048.62099 · doi:10.1214/ss/1056397487 |
| [4] | Goeman, A global test for groups of genes: Testing association with a clinical outcome, Bioinformatics 20 pp 93– (2004) · doi:10.1093/bioinformatics/btg382 |
| [5] | Härdle, Applied Nonparametric Regression (1990) · Zbl 0714.62030 · doi:10.1017/CCOL0521382483 |
| [6] | Hosmer, Applied Logistic Regression (2000) · Zbl 0967.62045 · doi:10.1002/0471722146 |
| [7] | Houwing-Duistermaat, Testing familial aggregation, Biometrics 51 pp 1292– (1995) · Zbl 0875.62515 · doi:10.2307/2533260 |
| [8] | Le Cessie, A goodness-of-fit test for binary regression models based on smoothing methods, Biometrics 47 pp 1267– (1991) · Zbl 0825.62833 · doi:10.2307/2532385 |
| [9] | Le Cessie, Testing the fit of a regression model via score tests in random effects models, Biometrics 51 pp 600– (1995) · Zbl 0825.62608 · doi:10.2307/2532948 |
| [10] | Lesaffre, Multiple-group logistic regression diagnostics, Applied Statistics 38 pp 425– (1989) · Zbl 0707.62151 · doi:10.2307/2347731 |
| [11] | Marcus, On closed testing procedures with special reference to ordered analysis of variance, Biometrika 63 pp 655– (1976) · Zbl 0353.62037 · doi:10.1093/biomet/63.3.655 |
| [12] | McCullagh, Generalized Linear Models (1989) · Zbl 0588.62104 · doi:10.1007/978-1-4899-3242-6 |
| [13] | Pigeon, An improved goodness-of-fit statistic for probability prediction models, Biometrical Journal 41 pp 71– (1999) · Zbl 0915.62036 · doi:10.1002/(SICI)1521-4036(199903)41:1<71::AID-BIMJ71>3.0.CO;2-O |
| [14] | Solomon, Approximations to density functions using Pearson curves, Journal of the American Statistical Association 73 pp 153– (1978) · doi:10.1080/01621459.1978.10480019 |
| [15] | Verweij, A goodness-of-fit test for Cox’s proportional hazards model based on martingale residuals, Biometrics 54 pp 1517– (1998) · Zbl 1058.62666 · doi:10.2307/2533676 |
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