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Jason Benedict - Thesis 2016.pdf (712.72 KB)

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Comparing the Hosmer-Lemeshow Goodness of Fit Test With Varying Number of Groups to the Calibration Belt in Logistic Regression Models

Benedict, Jason A
http://rave.ohiolink.edu/etdc/view?acc_num=osu1469186992

Abstract Details

2016, Master of Science, Ohio State University, Public Health.
Logistic regression is a commonly used statistical technique in business and the sciences when an outcome is binary. For example, clinical trials may employ a logistic regression model when an outcome is presence or absence of disease, or a business may use such a model when the outcome is the presence or absence of a customer’s purchase of a product. An ideal logistic regression model both discriminates well and is well-calibrated. A well-calibrated model is one where the predicted percentages of success are close to the observed percentages. The Hosmer-Lemeshow test is a commonly used goodness of fit test that is used to test the calibration of a logistic regression model. The Hosmer-Lemeshow test becomes too powerful as the sample size increases, and an adaptive equation was recently proposed by Paul et al. (2013) to recommend the number of groups to use as the sample size increases. A new method to test the calibration of a logistic regression model, the calibration belt, was recently proposed by Nattino et al. (2014). The purpose of this study is to compare the power of the calibration belt with the Hosmer-Lemeshow test through simulations of several models with differing deviations from the true model and various probabilities of success. The Hosmer-Lemeshow test is applied to the models with varying number of groups (from g=6 to g= 5000), including the number of groups recommended through the adaptive equation proposed by Paul et al. (2013). The type 1 error rate of the calibration belt and the Hosmer-Lemeshow test is also assessed in all of these models. The simulations show that the calibration belt is nearly always the most powerful test, but the type 1 error rate of the calibration belt is often significantly below the nominal rate of 5%. The Hosmer-Lemeshow test does not suffer from this problem. It is also shown that the adaptive group equation proposed by Paul et al. (2013) depends largely on the probability of success of each of the models.
Rebecca Andridge, PhD (Advisor)
Stanley Lemeshow, PhD (Committee Member)
40 p.
Biostatistics; Public Health
logistic regression; Calibration belt; goodness of fit; hosmer-lemeshow test

Recommended Citations

Citations

  • Benedict, J. A. (2016). Comparing the Hosmer-Lemeshow Goodness of Fit Test With Varying Number of Groups to the Calibration Belt in Logistic Regression Models [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1469186992

    APA Style (7th edition)

  • Benedict, Jason. Comparing the Hosmer-Lemeshow Goodness of Fit Test With Varying Number of Groups to the Calibration Belt in Logistic Regression Models. 2016. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1469186992.

    MLA Style (8th edition)

  • Benedict, Jason. "Comparing the Hosmer-Lemeshow Goodness of Fit Test With Varying Number of Groups to the Calibration Belt in Logistic Regression Models." Master's thesis, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1469186992

    Chicago Manual of Style (17th edition)

osu1469186992
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This open access ETD is published by The Ohio State University and OhioLINK.