4.7.3 Regression analysis to test cross-level interactions

A cross-level interaction is an interaction between a variable measured at the micro level and one measured at the macro level. Otherwise it is no different from a standard interaction effect in that we test for the interaction by considering the coefficient of a variable that is the product of two other variables. For example, suppose you are interested in whether trust in people in general has a stronger effect on trust in politicians in PR countries than elsewhere, then you could first create a variable which is the product of ppltrst and pr.

gen ppltrstXpr = ppltrst*pr

and then run the following regression with the new variable as the interaction term.

Example 9: Regression analysis to test cross-level interactions


. regress trstplt ppltrst pr ppltrstXpr

      Source |       SS       df       MS              Number of obs =    6148
-------------+------------------------------           F(  3,  6144) =  268.37
       Model |  3803.81214     3  1267.93738           Prob > F      =  0.0000
    Residual |  29028.2848  6144  4.72465573           R-squared     =  0.1159
-------------+------------------------------           Adj R-squared =  0.1154
       Total |  32832.0969  6147  5.34115779           Root MSE      =  2.1736

------------------------------------------------------------------------------
     trstplt |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     ppltrst |   .2969988   .0316635     9.38   0.000     .2349273    .3590703
          pr |   .0972149   .1745838     0.56   0.578    -.2450304    .4394603
  ppltrstXpr |   .0217259   .0338948     0.64   0.522    -.0447198    .0881715
       _cons |   2.168255   .1606279    13.50   0.000     1.853368    2.483141
------------------------------------------------------------------------------

The coefficient of ppltrstXpr is positive and statistically significant, indicating that the correlation between trust in people in general and trust in politicians is stronger in PR countries. Again this analysis doesn't take the clustering of people into different countries into account, and strategies to deal with this are discussed in Unit 6.

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