Empirical Analysis of Intersectionality

Dubrow, Joshua Kjerulf.  2008.  “How Can We Account for Intersectionality in Quantitative Analysis of Survey Data?  Empirical Illustration of Central and Eastern Europe.”  ASK: Society, Research, Methods 17: 85-102.

 

NOTE:  The Russian Federation– available in ESS Round Three – is a clear outlier in terms of social heterogeneity.  To simplify the empirical illustrations, I omit Russia from analyses that are unnecessarily complicated by such outliers.      

As the purpose of these illustrations is to propose analytical strategies with major demographic variables, I include only gender, ethnicity, and class, and their intersections, and do not include standard control variables (such as age, income, and education; see Dubrow et al 2008 and Gallego 2008). 

For the additive approach, the logistic regression equation can be expressed as:

log(p/1-p) = a + β₁g_ij + β₂e_ij + β₃c_3ij + r_ij       

where (p/1-p) is the probability the respondent engaged in soft political protest, i refers to individual,  j refers to the country, g refers to gender, e refers to ethnicity, and c refers to class; r is the error term. 

The model assumes that none of the explanatory variables — gender, ethnicity, and class — has a positive effect on soft political protest. This model accounts for cumulative disadvantage in a sense that β ₁ + β ₂ + β ₃ < 0.

Thus, the best way to use this equation is to (a) show that master categories have statistically significant negative effects on soft political protest and (b) determine the presence of cumulative disadvantage separable identities by adding up the coefficients.

Table 1 presents the effects of gender, ethnicity, and class on soft political protest for all and each of the Central and Eastern European countries of this study.  For all countries combined, gender, ethnicity and class are statistically significant and in a direction consistent with that of previous studies.  Any one of these identities decreases the probability of soft political protest. 

CLICK ON THE TABLE FOR THE FULL VIEW

 

With one exception the hypothesis that none of the explanatory variables — gender, ethnicity, and class — has a positive effect on soft political protest is supported: when coefficients are significantly different from 0, the signs are negative.  The exception is ethnicity in Hungary: ethnic minority is more involved in soft protest that the rest of the population.    Note that in Poland the size of ethnic minority is very small (1,05 percent), and the equation is estimated without that demographic variable.

 

The main result of this analysis is that the research hypothesis stating that β 1 + β 2 + β 3 < 0 has empirical support for all countries (-1,275), and individually for Bulgaria (-3,114), Estonia (-1,262), Hungary (-0,111), Poland (-1,117), Slovenia (-0,845), Slovakia (-0,531) and Ukraine (-1,889). 

 

The effect of particular categories depends on their distribution. To standardize their impact, I multiplied each coefficient by standard deviation of their respective variable (Kaufman 1996).  Table 2 provides semi-standardized coefficients and sum of them.  For all countries combined, semi-standardized coefficients reveal that if gender would be distributed in the same way as ethnicity, then gender would have a greater effect than ethnicity.  In ranking countries by the sum of their coefficients, there is no difference between Table 1 and Table 2.  There are differences in the relative impacts of some of the categories within countries.  Comparing standardized and unstandardized coefficients, in Ukraine class changes from having the second-most to the greatest level of disadvantage, and gender from last to second.        

Table 2  Semi-Standardized Effects of Gender, Ethnicity, and Class on Soft Political Protest for Central and Eastern European Countries and Their Sums

 

 

Country	Gender	Ethnic	Class	Sum
All	-0,153	-0,105	-0,275	-0,533
Bulgaria	-0,139	-0,494	-0,656	-1,289
Estonia	0,085	-0,264	-0,364	-0,543
Hungary	-0,119	0,130	-0,197	-0,186
Poland	-0,238	– a	-0,304	-0,542
Slovenia	-0,148	0,044	-0,300	-0,404
Slovakia	-0,156	0,002	-0,097	-0,252
Ukraine	-0,269	-0,159	-0,288	-0,716

 

Note:  Significant coefficients of at least p<0,10 in bold.

^a  Not calculated due to insufficient number of cases.

 

 

To compare the relative probabilities of soft political protest, Table 3 presents odds ratios of soft political protest for gender, ethnicity and class for Central and East Central Europe for both unstandardized (U) and semi-standardized (S) coefficients.  Substantively, the results are similar to that of Table 2, but the odds ratios provide a clear picture of relative probabilities among demographic categories.   For all countries combined, membership in disadvantaged class decreases probability the most (46 percent), followed by ethnicity (30 percent) and gender (26 percent).   Across countries, disadvantaged class membership leads to the largest decrease in protest probability — 48 percent, on average, which is twice that of the mean gender effect.  Some probabilities are particularly striking: In Bulgaria, disadvantaged class membership decreases probability by 78 percent, while in Hungary, ethnic minorities, even if they are women of a disadvantaged class, increases probability of protest by 17 percent. 

 

 

Table 3  Odds Ratios of Soft Political Protest for Gender, Ethnicity and Class for Unstandardized (U) and Semi-Standardized (S) Coefficients

 

	Gender		Ethnic		Class
Country	U	S	U	S	U	S
All	0,735	0,858	0,704	0,900	0,540	0,760
Bulgaria	0,753	0,870	0,274	0,610	0,215	0,519
Estonia	1,186	1,089	0,561	0,768	0,425	0,695
Hungary	0,786	0,888	1,730	1,139	0,658	0,821
Poland	0,621	0,788	–a	–a	0,527	0,738
Slovenia	0,742	0,862	1,261	1,045	0,459	0,741
Slovakia	0,731	0,855	1,005	1,002	0,800	0,908
Ukraine	0,580	0,764	0,486	0,853	0,536	0,750

Note:  Significant coefficients of at least p<0,10 in bold.

^a  Not calculated due to insufficient number of cases

 

In the multiplicative approach, intersectionality implies that the relationship between the person and the attitude or behavior is conditional upon intersecting identities.   In interaction effects the relationship between the constituent elements of the explanatory variables is changed with the introduction of a third variable: “the association appears under certain conditions, and it disappears or changes in intensity or direction when other conditions happen” (Agresti and Finlay 1999: 369).   In this version, to test for intersectionality, interaction terms are required (Brambor et al 2006; Weldon 2006: 242-244; McCall 2005: 1787-1788; Bowleg 2008).

 

 

Using interaction terms for testing intersectionality theory involves a couple of complications. First, significance of interaction terms depends on the size of the main effects.  Since main effects, more often than not, should be included in the model along with the interaction terms (Brambor et al 2006), the chance of finding empirical support for intersectionality theory is reduced.  However, a sufficiently large sample size can improve chances of discovering significance of interaction terms. 

 

 

Another complication is that intersectionality frequently calls for more than two variables.  Interactions of higher order, i.e. more than two variables, must be considered.  Interpretations of a single equation with higher order and lower order interactions can be tricky and great care must be taken in interpreting them (Braumoeller 2004: 810).

 

 

Interaction effects are expressed through cross-product terms created by multiplying two or more of the explanatory variables together.  In this case we have the following interactions: gender-ethnicity, gender-class, ethnicity-class, and gender-ethnicity-class.  First three interactions are of the second order, and the second is of the third order. Accordingly the logistic regression equation can be expressed as,

 

 log(p/1-p) = a + β₁g_ij + β₂e_ij + β₃c_3ij + β₄(ge)_ij + β₅(gc)_{i j} + β₆(ec)_{i i} +  β₇(gec)_ij + r_ij 

 

As omitting lower order interactions can produce biased results, all possible interactions from this combination of demographics are included in the model (Βraumoeller 2006: 811).  Thus we can formulate the following research hypotheses:

            β₁+ β₂ + β₄ < 0

            β₁ + β₃ + β₅ < 0

            β₂ + β₃ + β₆ < 0

and      β₁ + β₂ + β₃ + β₄ + β₅ + β₆(ec)_{i i}+  β₇ < 0

            Table 4 shows all these hypotheses are supported by the data.

 

 

Table 4.  Logistic Regression of Soft Political Protest on Gender, Ethnicity and Class, Including Interactions, for Central and Eastern European Countries

 

	B	SE		EXP(B)
Gender	-0,298**	0,059		0,742
Ethnic	-0,643**	0,168		0,526
Class	-0,567**	0,088		0,567
Interactions
Gender – Ethnic	0,453*	0,222		1,573
Gender – Class	-0,165	0,136		0,848
Ethnic – Class	0,566*	0,284		1,761
Gender – Ethnic – Class	-0,764†	0,439		0,466
Constant	-1,260**	0,043		0,284
Log Likelihood    10141,570 Chi2                                 156,924** N                          11371

** p<0,01 *p<0,05 †p<0,10

 

Total effect of all variables is statistically significant.  Interpreting the total effect of particular intersections with unstandardized coefficients, all intersections, including ethnic – class (β2 + β3 + β6 = -0,556), decreases probability of protest.  Cumulative disadvantage is evident, as the higher order interaction decreases probability of protest more (72 percent) than any of the lower order terms (e.g. gender-class reduces probability by 62 percent).  Gender-ethnic-class variable is remarkable as coefficients for three-way interactions are rarely as robust.   

 

 

As this is a cross-national study, controlling for country effects is important.  Table 5 presents results from a  logistic regression of the response variable on gender, ethnicity and class, including interactions and country effects, with the Russian Federation in the reference category.  Substantive changes are for particular countries.  In comparison with Russia, the country effect of some increase probability of protest (Estonia, Hungary, Slovenia, Slovakia and Ukraine) and for others it decreases (Bulgaria and Poland).  The gender-ethnic intersection actually increases probability in Slovenia (0,081) and Slovakia (0,056).  In Bulgaria, the gender-ethnic-class intersection decreases probability by 75 percent.

 

 

A graph clearly displays cumulative disadvantage and relative impact of intersections. I constructed a variable that measures how many disadvantaged categories a respondent has that ranges from zero (no disadvantage identity) to three (having all three disadvantaged identities).  Figure 1 presents the predicted probabilities of soft political protest for each category of the variable.  Distance between demographics within each category corresponds to the coefficients in Table 4.  This graph clearly illustrates (a) the huge gap in protest probability between those with no disadvantaged identities and those with all three, (b) the cumulative effects of disadvantage on protest probability, and (c) relative disadvantage between types of intersections.   

 

Figure 1.  Predicted Probability of Soft Political Protest by Respondent’s Number of Disadvantaged Identities

 

Legend: g = gender, e = ethnicity, c = class

 

While the strictest version of intersectionality theory — the anticategorical approach — suggests different statistical methods, the procedures that created Figure 1 can be fruitfully applied to it.  A common way to address the anticategorical approach is by analysis of subsamples, i.e. creating separate datasets for each intersection and performing statistical analyses on them.  In this empirical illustration, this means conducting z-tests on the percentage of each intersection that engages in protest.  The results from this analysis are not substantially different from that presented in Figure 1, and as such I advocate conducting the multiplicative model as outlined above instead of analysis of subsamples.

 

Note, however, that there are several problems with applying the anticategorical approach to multivariate regression. Theoretically, according to the anticategorical approach, main effects are fictional demographic categories that obscure the influence each full-bodied intersection has on the response variable.  Thus, the constituent elements of the interaction terms do not have meaning in and of themselves, and this approach would exclude them from the equation.  Applying this may have severe consequences for multivariate regression models.  When main effects are not included along with interaction terms the model may have misspecification error.  Strong statistical or theoretical conditions for not including main effects must be present, and these conditions are rarely met (Brambor et al 2006: 66 – 71).  Since anticategorical approaches advocate inductive methods, i.e. theory obscures discovery (Hancock 2007: 67), there are no strong theoretical grounds.  There may be statistical grounds, and this requires a careful checking of multicollinearity diagnostics.  In general, such a model is too risky, and therefore should be a rarity.