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 groupRobinson (1950) – „Ecological fallacy“ Lazarsfeld, Menzel (1961) - On the relation

between individual and collective properties Iversen (1991) – Contextual analysisAnd many others…about multilevel

modeling

Three possible strategieshow 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

y = 5000 + 950x

5000

10000

15000

20000

25000

30000

0 5 10 15 20 25

years of education

inco

me

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)

5000

10000

15000

20000

25000

30000

0 5 10 15 20 25

years of education

inco

me

male

femalemale+female

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 studiesGoal: 1. to find common result of all covered studies and 2. to find reason of differences between studies

Cross classified modelsIndividual 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 – USAPISA, 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 informationZ-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)