By Werner Vach (auth.)
In many parts of technology a easy job is to evaluate the impact of numerous elements on a volume of curiosity. If this volume is binary logistic, regression types supply a robust instrument for this function. This monograph provides an account of using logistic regression within the case the place lacking values within the variables hinder using average innovations. Such occasions happen usually throughout a variety of statistical purposes.
The emphasis of this publication is on tools relating to the classical greatest chance precept. the writer stories the necessities of logistic regression and discusses the range of mechanisms which would reason lacking values whereas the remainder of the booklet covers the equipment that could be used to accommodate lacking values and their effectiveness. Researchers throughout a number disciplines and graduate scholars in information and biostatistics will locate this a readable account of this.
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Extra info for Logistic Regression with Missing Values in the Covariates
Example text
Nevertheless we have to expect that CPI results in biased estimates. However, UPI must be regarded as a much worse approximation, and hence we expect that the bias oi UPI is larger than the bias of CPI. Only if Xl and X 2 are independent, UPI seems to be as appropriate as CPI. Even if we yield nearly unbiased estimates, it remains the problem of the underestimation of variance. In the formula of the asymptotic variance of the the PML estimate the second term represents a correction due to the estimation of 1r.
1). First in a logistic model maximum likelihood estimates of an effect without adjustment for additional covariates are more precise than maximum likelihood estimates with adjustment (Robinson & Jewell 1991) and second the maximum likelihood estimates based on complete data are more precise than the maximum likelihood estimates based on incomplete data. Hence considering Omission of Covariate as a tool to handle missing value the bias of the estimation is accompanied with a tendency to smaller confIdence intervals.
Fillillg (32 = 0, the loss vanishes. 8): No loss under MCAR, substantial loss otherwise. Note that here even the joint restriction p = 0 and (32 = 0 does not prevent a loss of efficiency. The influence of the variation of the observation rates on the efficiency of Filling has been also observed by Wild (1991) for the situation of completely missing covariate information. Also the simulation results of Zhao & Lipsitz (1992) demonstrate the possible loss of efficiency. 7: Asymptotic relative efficiency with respect to the estimation of (31 between ML Estimation and Filling.