| 摘要: |
| 对于糖尿病数据，利用单指标部分含扭曲测量误差的部分变系数单指标模型进行拟合，由于实验数据的维数较大，相较于传统的参数模型和非参数模型，应用半参数模型不仅可以较好地拟合数据，还可以避免“维数灾祸”问题；此外，如果在拟合时忽略误差的影响，可能导致模型估计产生偏差，因此，进一步选择体质指数（BMI）作为潜在的混淆因子，并假设响应变量和单指标变量均受到BMI的乘积污染；观察实验结果发现：6种血清指标测量数据和性别的系数会随着BMI的变化而变化，并且对比带有测量误差和不含测量误差两种情形下的结果发现，糖尿病人定量测量值、年龄和平均血压均受到BMI的污染；这些结果说明选择单指标部分带有测量误差的部分变系数单指标模型对该数据集进行拟合是合理的，并且相较于不含测量误差的半参数模型，可以更好地挖掘数据中的信息。 |
| 关键词: 部分变系数单指标模型 乘积扭曲测量误差 糖尿病数据 |
| DOI： |
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| Research on Diabetes Data Based on Semi parametric Model with Measurement Error |
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SUN Xing, HUANG Zhen-sheng
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School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
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| Abstract: |
| For diabetes data, the partially varying-coefficient single-index model with distorted measurement error was used for fitting. Due to the large dimension of experimental data and compared with the traditional parametric model and non parametric model, the application of semi parametric model can not only fit the data better, but also avoid the problem of “curse of dimensionality”. In addition, if the influence of error is ignored during fitting, it may lead to deviation in model estimation. Therefore, body mass index (BMI) was further selected as a potential confounding factor, and it was assumed that both the response variable and the single index parameter were contaminated by the BMI. The observation of the experimental results showed that the coefficient of the measurement data of the six serum indicators and sex would vary with BMI, and comparing the results in two different situations, it can be found that the quantitative measurement value, age and average blood pressure of diabetic patients were all polluted by BMI. These results indicate that it is reasonable to select the partially varying coefficient single-index model with measurement error for the fitting of this data set, and compared with the semi-parameter model without measurement error, this semi-parametric model can better mine the information in the data. |
| Key words: partially varying-coefficient single-index model product distortion measurement error diabetes data |
