Comparing (Ordinary) Multilevel Modeling with Multilevel Structural Equation

Modeling

Michael Braun

GESIS – Leibniz Institute for the Social Sciences,

Mannheim

Overview

The substantive research question Two statistical models Results Conclusions

The substantive research question

anomalies found for item on civil disobedience in ISSP 2004 battery on rights in a democracy

in one group of countries, values for civil disobedience markedly lower than for index of rights in a democracy, excluding this item

suspicion this might be related to satisfaction with democracy (then civil disobedience not necessary or even harmful)

There are different opinions about people’s rights in a democracy. On a scale of 1 to 7, where 1 is not at all important and 7 is very important, how important is it …

a. that all citizens have an adequate standard of living

b. that government authorities respect and protect the rights of minorities

c. that government authorities treat everybody equally regardless of their position in society

d. that politicians take into account the views of citizens before making decisions

e. that people be given more opportunities to participate in public decision-making

f. that citizens may engage in acts of civil disobedience when they oppose government actions

Civil disobedience item vs. index (items a-e)

CountryCivil

DisobedienceIndex (without

civ.dis.)

Canada 3.8 6.2

Denmark 4.1 6.4

United States 4.0 6.4

Western Germany 5.3 6.3

Eastern Germany 5.5 6.4

Hungary 5.6 6.3

Spain 5.1 6.6

Two statistical models

(Ordinary) 3-level Multilevel Modeling Multilevel Structural Equation Model (ML-SEM)

allowing for direct effects of satisfaction with democracy as covariate on items, given the common factor

3-level multilevel model

dependent variable: evaluation of any of the six items on rights in a democracy.

that is: in addition to respondent and country level, there is an item level, which constitutes the lowest level.

3-level multilevel model

Country 1 Country 2

Respondent 1 Respondent 2 Respondent 1 Respondent 2

Standard of living

Rights of minorities

Equality of treatment

Respon-siveness

Participa-tion

Civil dis-obedience

… …

…

3-level multilevel model The following variables are included : Indicators for the second to sixth item (main effects

on the item level) Satisfaction with democracy both on the individual

and on the country level (main effects on the individual and country level, respectively)

Interactions of the indicators for the second to sixth item with satisfaction with democracy – both on the individual and country level (cross-level interactions)

3-level multilevel model

Main effects

rights of minorities -9.6

equality of treatment .08

responsiveness -.06

participation 2.2

civil disobedience 23.6

Satisfaction with democracy (individual level)

6.3

Satisfaction with democracy (country level) -2.1

3-level multilevel model

Interactions with satisfaction (individual level) rights of minorities 3.9

equality of treatment 3.5

responsiveness -4.8

participation -7.8

civil disobedience -22.2

3-level multilevel model

Interactions with satisfaction (country level) rights of minorities 1.6

equality of treatment -.7

responsiveness 2.4

participation -5.2

civil disobedience -45.2

Constant 6.69

Country-level variance .035

Respondent-level variance .471

Response-level variance 1.169

3-level multilevel model

Main results: [from model with only item identifiers:]Civil

disobedience has high item difficulty. The higher satisfaction with democracy on the

individual level the higher the support for rights in democracy in general.

The higher satisfaction with democracy on the country level the lower the support for rights in democracy in general (borderline effect).

3-level multilevel model

The higher satisfaction with democracy on the individual level the lower agreement with civil disobedience.

The higher satisfaction with democracy on the country level the lower agreement with civil disobedience.

Multilevel SEM

The following variables and relationships are included :

the six indicators as measures of common factors on the individual and on the country level

regressions of the factors (on both the individual and on the country level) on satisfaction with democracy on the individual and country level, respectively

Multilevel SEM

regressions of the second to sixth indicator of the common factors on satisfaction with democracy both on the individual and on the country level

Multilevel SEM

Satisfaction d.

1.0* 1.29* 0.89* 0.66* 0.60* 0.18

Between level

Within level

0.05 -0.00 -0.00 -0.09* -0.49*

-0.06

Standard liv. R. minorities Equality of t. Responsiveness Participation Civil disobedience

1.0* 1.18* 1.13* 1.17* 1.20* 0.89*

0.02

0.01 0.01* -0.02* -0.03* -0.07*

Rights

Satisfaction d.

Standard liv. R. minorities Equality of t. Responsiv. Ci vil disobed.Participation

Rights

Multilevel SEM

loading of civil disobedience on the factors suspicious, particularly on the country level

regression of the common factors on the individual and the country level not significant

small negative direct effect of satisfaction with democracy on civil disobedience (given the common factor) on the individual and stronger negative direct effect on the country level

Conclusions

conclusions similar with regard to mean of civil disobedience, with regard to interaction with satisfaction with democracy

loading of civil disobedience on the individual level not really suspicious in multilevel CFA

positive effect of satisfaction with democracy on the individual and negative on the country level on attitudes towards rights in a democracy not significant in multilevel CFA

Conclusions

Question: Which modeling strategy is best?

Thank you!