Advanced Lazarsfeldian Methodology Conference From Lazarsfeldian Contextual analysis to Multilevel models (Strategies for analysis of individual and/or aggregate data) Petr Soukup

Basic „ideology“ §Gauss (1805) – „Regression analysis, OLS“ §Homans (1950) - Human group §Robinson (1950) – „Ecological fallacy“ §Lazarsfeld, Menzel (1961) - On the relation between individual and collective properties §Iversen (1991) – Contextual analysis §And many others…about multilevel modeling

Three possible strategies how to analyse data

Three possible strategies to analyze individual and/or aggregate data §Analyze only individual data (classical regression or correlation analysis) §Analyze only aggregate data (but Robinson’s problem and EI solution) §Analyze individual and aggregate data at once (contextual and multilevel analysis)

Individual level data only

1st possible strategy (only individual data) §We omit information about aggregate levels (groups etc.), we loose some explained variance §We use classical regression or correlation analysis and many other methods §We make some statistical mistakes by ignoring of some dependencies of observations (or by pretending of the independence) §Results are usually quite good but we are not able differentiate between aggregate levels §If we have individual and aggregate data this is only 2nd best strategy

Results for 1st strategy §The result is one regression line (one equation). This equation is the same for all individuals („average“ line).

Inference from aggregate data

2nd possible strategy (only aggregate data) §We omit/do not have information about individual level §We want to infer about individual behaviour §We can make crucial mistakes (Robinson’s problem) so called ecological fallacy (demonstration in the inference about relation of education and salary)

2nd possible strategy (only aggregate data) §Ecological fallacy solution = ECOLOGICAL INFERENCE §50-ties method of bounds (Duncan, Davis, 1953), ecological regression (Goodman, 1953, 1959) §90-ties King: A solution to the ecological inference problem (1997) §General solution can not be found (we always loose information by aggregation), current solutions are only specific ones

Aggregate(groups) + individual data

Picture 4 (Different intercepts and slopes)

Lazarsfeldian approach §[Lazarsfeld, Menzel 1961] – typology of variables §1) global, 2) relational, 3) contextual –individual level §4) analytical and 5) structural – aggregate level § Examples of these types §Warning: This is „reduced“ version of original typology §4) can be derived from 1) by aggregation §5) can be derived from 2) by aggregation §3) can be derived from 1) or 2) measured on aggregate level by disaggregation

Lazarsfeldian approach §This process (aggregation and disaggregation) can have of course more than two levels up to infinity (in practical analyses two or three levels) §The name Contextual analysis – we use information about aggregate data if we analyse individual data §We use currently multilevel analysis based on lazasfeldian contextual ideas

Contextual/multilevel analysis

Problem with group/context §Group boundaries –sometimes can be fuzzy, it is difficult to decide whether somebody is member of group or not §Mobility between groups – people tend to change group membership (change of school, neighborhood, church etc.) – „new“ members are not influenced by the group at the same level as the old ones §Multiple membership (overlapping) – People are usually members of more than one group, we should work with more contexts, (Whoch context(s) is (are) the most important? (possible solution see slide Other problems that can be solved via ML models)

Two types of contextual analysis §Interaction variables for individuals and groups (Method 1), or §A two-step estimated model based on variables measured at the first level for individual contexts, and then by using these estimates at the second level in the role of dependent variables (Method 2).

Multilevel analysis §Inclusion of random error at the second (group) level §Estimates by iterative methods §More precise estimates (lower standard errors)

Multilevel approach as more general Growth models §We measure characteristic of individuals many times. We can treat measurements in current time as first level (similar to pupils at schools) and individuals as second levels (similar to school). „Average“ growth curve is one result of analysis but second result can be description (or explanation) of differences of individual growth curves. Metaanalysis §1st level data from individual studies §2nd level individual studies Goal: §1. to find common result of all covered studies and §2. to find reason of differences between studies Cross classified models Individual can be included in more than one group, these group are not hierarchically nested. and their influences are mixed (crossed)

Conclusion?

Real research - examples §HSB – USA §PISA, TIMMS or ICCS internationally

Model for multilevel analysis i- index for individual, j-index for group Lowest (individual) level: (1)Yij= b0j+ b1jXij+ eij, X-individual variable and at the Second (group) level: NEW (2) b0j= g00+ g01Zj+ u0j Random parts at the second level (3) b1j= g10+ g11Zj+ u1j because we do not have information Z-group variable about all groups!!! Combining individual and group level: (1)+(2)+(3): Yij= g00 + g10Xij+ g01Zj+ g11ZjXij -fixed part + u1jXij+ u0j+ eij -random part (random coefficient model see Hox, 2002)