Methodology
Multilevel regressions, sides of field research
Multilevel Regression Models
To study democracy and world economic development I conducted a longitudinal analysis with hierarchically structured data, where hierarchical models were expressed in the form of growth models.
The modeling was implemented in "SAS PROC MIXED”. In the simplest form (without added predictors), the two-level growth model is expressed as the sum of two parts: a fixed part with two fixed effects (for the intercepts and for the effect of time) and a random part, which contains estimates of variances for the intercepts, the time slope, the covariance, and the residual. The following equation summarizes the simplest form of the two-level hierarchical growth model employed:
Y_{ij} = (β_{00} + β_{10} Year_{ij})+ (e_{oj} + e_{1j} Year_{ij} + r_{ij}),
where e_{oj} ~ N(0, τ_{00}) e_{1j} ~ N(0, τ_{10}) r_{ij} ~ N(0, σ^{2})
β_{00} | represents an average democracy level in the world in 1950 |
β_{10} Year_{ij} | represents an average slope of democratic growth in the world |
τ_{00} | represents variation in the democracy level among countries (between countries' intercepts) |
τ_{10} | represents variation among countries' temporal rate of democratic growth (among countries' slopes) |
σ^{2} | represents residual (the within country variance) |
ij | the subscript denotes the within country level (the level-1) |
j | the subscript denotes the country or region level (level-2) |
Hence, a model with a level-1 and level-2 covariate could be summarized by the following equation:
Y_{ij} = [β_{00} + β_{10} Year_{ij} + β_{01} X_{ij} + β_{11} (X_{ij})(Year_{ij}) + β_{01} X_{j} + β_{11} (X_{j}) (Year_{ij})]+[e_{oj} + e_{1j}(Year_{ij}) + r_{ij}]
With the variance in democratic level and the rate of democratic growth among regions added to this model, the above two-level model became a three-level growth model to which more covariates were added. Detail explanation of this modeling is attached.
Multilevel Regression
Methodology questionnaire
Field research and research sides
In additional to the multilevel statistical analyses, conducted studies used field research interviews and observation to support findings of statistical research. The data were collected using standardized interviews of men and women in six democratizing countries of Hungary, Poland, Ukraine, Kyrgyzstan, Mali and Senegal, in 2000-2004. I also conducted research in India and Zambia. I used uniformed questionnaire, translated to a particular country’s language and retranslated to English used in this research.