Jackknifing in Categorical Data Analysis

Estimation of nonlinear functions of a multinomial parameter vector is necessary in many categorical data problems. The first and second order jackknife are explored for the purpose of reduction of bias. The second order jackknife of a function g(.) of a multinomial parameter is shown to be asymptotically normal if all second order partials ?²g( p )?dp_i?p_j obey a Hölder condition with exponent α>1/2. Numerical results for the estimation of the log odds ratio in a 2times2 table demonstrate the efficiency of the jackknife method for reduction of mean-square-error and the construction of approximate confidence intervals.     

The Interaction Between Role Structures and Self-Conceptions in Fostering Different Types of Self-Esteem in Innovative and Traditional Elementary Schools*

A two-dimensional model of inner and outer self-esteem is discussed wherein inner self-esteem is hypothesized to be an outcome of self-evaluations of performance in prominent role identities. Outer self-esteem is hypothesized to be related to self-evaluations of both prominent and nonprominent role identities. The research context is a comparison of the different processes facilitating self-esteem in innovative schools (emphasis on student-initiated activities and control) and traditional (emphasis on pre-determined curriculum and teacher-administrator control). Data across school type demonstrate a modest correlation between positive self-evaluations of performance in prominent role identities and both types of self-esteem. The data suggest that high evaluation of performance in nonprominent role identities is related to outer self-esteem but not to inner self-esteem. Further empirical clarification of the concepts was established by viewing the relationships within school type. In the innovative schools both types of self-esteem were predominantly related to positive evaluations of prominent role identities, whereas in the traditional schools both types of self-esteem were related to both performance in prominent and nonprominent role identities. Thus the theoretical distinction gained partial support while the process of gaining self-esteem was shown to be essentially different between alternate school structures. Controls for social desirability, race, sex, and father's occupation did not change these findings.