MULTILEVEL INVESTIGATIONS OF SYSTEMATICALLY VARYING SLOPES: ISSUES, ALTERNATIVES, AND CONSEQUENCES

Publisher Summary This chapter discusses the issues, alternative, and consequences of mul;tilevel investigations of systematically varying slopes. Generally, the situations of interest are large-scale non-experimental studies of educational effects. The focus may be on either the program—for example, curricular innovation, school type—the school, the classroom/teacher, or some combination, as the sources of educational effects. Regardless, the intent is to identify the antecedents of student performance and attitude and estimate the magnitude of their effects. The typical study involves two-stage sampling. Either a sample, which can be random, representative, or convenience, of schools is drawn and students are sampled randomly or on a stratified random basis from within schools. Alternatively, a sample of classrooms is chosen, either randomly or exhaustively within a sample of schools, and all the students within the classrooms comprise the total study sample. In either case, this situation yields data with dependencies among observations within the first-stage sampling units; that is, there are correlations among individuals in the same macro units.

[1]  H. Goldstein Multilevel mixed linear model analysis using iterative generalized least squares , 1986 .

[2]  Eric A. Hanushek,et al.  Efficient Estimators for Regressing Regression Coefficients , 1974 .

[3]  Anthony S. Bryk,et al.  A Hierarchical Model for Studying School Effects , 1986 .

[4]  W. S. Robinson Ecological correlations and the behavior of individuals. , 1950, International journal of epidemiology.

[5]  David E. Wiley The Design and Analysis of Evaluation Studies. , 1969 .

[6]  Jan de Leeuw,et al.  Random Coefficient Models for Multilevel Analysis , 1986 .

[7]  E. Thorndike,et al.  On the Fallacy of Imputing the Correlations Found for Groups to the Individuals or Smaller Groups Composing Them , 1939 .

[8]  Murray Aitkin,et al.  Statistical Modelling of Data on Teaching Styles , 1981 .

[9]  Noreen M. Webb,et al.  Between-class and within-class effects in a reported aptitude * treatment interaction: Reanalysis of a study by G. L. Anderson. , 1975 .

[10]  J. Douglas Willms,et al.  School Effectiveness Within the Public and Private Sectors , 1984 .

[11]  Barbara Entwisle,et al.  Contextual analysis through the multilevel linear model. , 1983 .

[12]  Leigh Burstein,et al.  Analyzing Multilevel Data in the Presence of Heterogeneous Within-Class Regressions , 1978 .

[13]  Leigh Burstein,et al.  Estimation from Grouped Observations , 1974 .

[14]  D. Lindley,et al.  Bayes Estimates for the Linear Model , 1972 .

[15]  Leigh Burstein,et al.  Measurement and Statistical Issues in Multilevel Research on Schooling , 1985 .

[16]  Donald B. Rubin,et al.  Empirical bayes estimation of coefficients in the general linear model from data of deficient rank , 1983 .

[17]  Jan-Eric Gustafsson ATTITUDES TOWARDS THE SCHOOL, THE TEACHER, AND CLASSMATES AT THE CLASS AND INDIVIDUAL LEVEL , 1979 .

[18]  Wolfgang Schneider,et al.  Classroom Differences in the Determination of Achievement Changes , 1984 .

[19]  L. Erbring,et al.  Individuals and Social Structure , 1979 .

[20]  M. Aitkin,et al.  Statistical Modelling Issues in School Effectiveness Studies , 1986 .

[21]  Louise Ryan,et al.  Weighted Normal Plots , 1985 .

[22]  Maureen T. Hallinan,et al.  A Reconceptualization of School Effects. , 1977 .

[23]  H. M. Walker A note on the correlation of averages. , 1928 .

[24]  R. L. Prentice,et al.  A case-cohort design for epidemiologic cohort studies and disease prevention trials , 1986 .