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Cephalo-Pelvic Disproportion Data with Collinearities

In: New Theory of Discriminant Analysis After R. Fisher

Author

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  • Shuichi Shinmura

    (Seikei University, Faculty of Economics)

Abstract

I discriminate the cephalo-pelvic disproportion (CPD) data. These data have a significant relationship with the Theory (1) We evaluated a heuristic OLDF by these data. However, we could only evaluate a six-variable model because our CPU power was poor and because of the limitations of a heuristic OLDF. Therefore, we could not extend our research. (2) These data consist of 240 patients with 19 independent variables. We specified three collinearities in these data and established how to remove such collinearities. (3) We found a strange trend of NMs by QDF and found that QDF is fragile for collinearities. Moreover, NM of Fisher’s LDF did not decrease in the 19 models from the one-variable model to the 19-variable model selected by the forward and backward stepwise procedure. On the other hand, NMs of our three MP-based optimal LDFs (OLDFs) decreased. (4) In the CPD data, we determined that a four-variable model is useful by the regression model selection procedure (plug-in rule1). However, the new model selection procedure that uses Method 1 recommends a nine-variable model as the best model. We believe that many variables and/or collinearities cause this difference. Because the Iris data have four variables and can satisfy Fisher’s assumption, the model selection procedure by regression analysis and the best model select the full model of seven LDFs, which are Revised IP-OLDF, Revised LP-OLDF, Revised IPLP-OLDF, SVM4 and SVM1, Fisher’s LDF, and logistic regression. This fact is the reason we should no longer use the Iris data as the evaluation data. (5) CPD data have many OCPs. This fact implies that Revised IP-OLDF can search for the several OCPs with the same MNMs and different coefficients groups that belong to different OCPs. This result means that it is difficult for us to evaluate the 95 % CI of discriminant coefficients. In this chapter, we solve these problems by the 100-fold cross-validation for small sample method (Method 1) and the best models of seven LDFs.

Suggested Citation

  • Shuichi Shinmura, 2016. "Cephalo-Pelvic Disproportion Data with Collinearities," Springer Books, in: New Theory of Discriminant Analysis After R. Fisher, chapter 0, pages 57-80, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-2164-0_3
    DOI: 10.1007/978-981-10-2164-0_3
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