12. Cross-Classified Models EPSY 8268 Cross-Classification Many cases exist where the units of observations belong to multiple higher-level units simultaneously. For example, students live in neighborhoods and attend schools, or students may have two different teachers simultaneously. Another example includes patients working with doctors and hospitals where hospitals take referrals from multiple doctors and doctors refer patients to various hospitals. Such models allow for a variety of analysis goals: Partition variance among students, schools, and neighborhoods Investigate the roles of characteristics of neighborhoods and schools Investigate the extent to which the associations between student characteristics and outcomes vary over neighborhoods and schools Estimate the unique effects of neighborhoods and schools Level-1 Model within cell + where ~ N(0, 2) Yijk eijk eijk = π0jk A model for outcome for case nested within row and column of a two-way classification. y i j k is the expected value of within cell (neighborhood × school). In this case is the π0jk Yijk jk eijk unique child effect, the deviation of the score for child from the cell mean, and 2 is the within ijk cell variance. Level-2 Models between cell = + + where ~ N(0, and ~ N(0, b00j c00k b00j c00k π0jk θ0 τb00) τc00) is the grand mean of Y θ0 is the neighborhood effect, averaged over all schools b00j j is the school effect, averaged over all neighborhoods c00k k Neighborhood by School Crosstabulation (a sample of Schools & Neighborhoods) Neighborhood School ID Total ID 0 3 5 8 15 16 17 18 19 20 29 0 0 0 0 0 0 0 1 0 8 9 32 0 0 0 0 0 0 0 1 0 5 6 38 0 0 0 0 0 0 0 1 0 4 5 39 0 0 0 0 0 0 0 1 0 2 3
12. Cross-Classified Models EPSY 8268 Cross-Classification Many cases exist where the units of observations belong to multiple higher-level units simultaneously. For example, students live in neighborhoods and attend schools, or students may have two different teachers simultaneously. Another example includes patients working with doctors and hospitals where hospitals take referrals from multiple doctors and doctors refer patients to various hospitals. Such models allow for a variety of analysis goals: Partition variance among students, schools, and neighborhoods Investigate the roles of characteristics of neighborhoods and schools Investigate the extent to which the associations between student characteristics and outcomes vary over neighborhoods and schools Estimate the unique effects of neighborhoods and schools Level-1 Model within cell Yijk = π0jk + eijk where eijk ~ N(0, 2) A model for outcome y for case i nested within row j and column k of a two-way classification. π0jk is the expected value of Yijk within cell jk (neighborhood × school). In this case eijk is the unique child effect, the deviation of the score for child ijk from the cell mean, and 2 is the within cell variance. Level-2 Models between cell π0jk = θ0 + b00j + c00k where b00j ~ N(0, τb00) and c00k ~ N(0, τc00) θ0 is the grand mean of Y b00j is the neighborhood j effect, averaged over all schools c00k is the school k effect, averaged over all neighborhoods Neighborhood by School Crosstabulation (a sample of Schools & Neighborhoods) Neighborhood ID School ID Total 0 3 5 8 15 16 17 18 19 20 29 0 0 0 0 0 0 0 1 0 8 9 32 0 0 0 0 0 0 0 1 0 5 6 38 0 0 0 0 0 0 0 1 0 4 5 39 0 0 0 0 0 0 0 1 0 2 3
12.Cross-classified-models.docx