GVPT 722: Example of Testing for and Dealing with Multicollinearity (2004 NES Data)(1) Regression of Bush thermometer rating on party identification, ideologicalidentification, demographic characteristics, and various measures of religiouscommitment (all variables coded to range from 0 to 1):. reg bushft partyid ideology educ income south white age sex prayer chattend guidance Source | SS df MS Number of obs = 800-------------+------------------------------ F( 11, 788) = 99.79 Model | 547295.938 11 49754.1762 Prob > F = 0.0000 Residual | 392882.261 788 498.581549 R-squared = 0.5821-------------+------------------------------ Adj R-squared = 0.5763 Total | 940178.199 799 1176.69362 Root MSE = 22.329------------------------------------------------------------------------------ bushft | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- partyid | 61.96001 2.862532 21.65 0.000 56.34092 67.5791 ideology | 20.65632 4.271697 4.84 0.000 12.27107 29.04157 educ | -11.97068 3.346378 -3.58 0.000 -18.53955 -5.401815 income | 4.170574 3.39353 1.23 0.219 -2.490855 10.832 south | 3.008949 1.755247 1.71 0.087 -.4365638 6.454461 white | -1.686565 2.012675 -0.84 0.402 -5.637402 2.264273 age | 5.853645 3.586434 1.63 0.103 -1.18645 12.89374 sex | .6461887 1.652344 0.39 0.696 -2.597328 3.889706 prayer | 3.212253 3.517829 0.91 0.361 -3.693172 10.11768 chattend | -5.793167 3.118907 -1.86 0.064 -11.91552 .3291821 guidance | 6.915486 3.087823 2.24 0.025 .8541547 12.97682 _cons | 10.99297 3.512615 3.13 0.002 4.097785 17.88816------------------------------------------------------------------------------(2) Bivariate correlations between religious commitment items. corr prayer chattend guidance(obs=1182) | prayer chattend guidance-------------+--------------------------- prayer | 1.0000 chattend | 0.5649 1.0000 guidance | 0.6983 0.5961 1.0000(3) Computing tolerance statistics (1/VIF). vif Variable | VIF 1/VIF -------------+---------------------- guidance | 2.35 0.424676 prayer | 2.32 0.431666 chattend | 1.84 0.544612 ideology | 1.80 0.556172 partyid | 1.66 0.601392 income | 1.29 0.775281 educ | 1.25 0.801983 white | 1.22 0.820536 age | 1.10 0.910830 sex | 1.09 0.913278 south | 1.08 0.923959-------------+---------------------- Mean VIF | 1.55(4) Creating an index of religious commitment (since all variables now range from 0 to1, just add them together, then divide again by 3 to get back to 0 to 1):. gen relcommit=chattend+guidance+prayer(30 missing values generated). summ relcommit Variable | Obs Mean Std. Dev. Min Max-------------+-------------------------------------------------------- relcommit | 1182 1.57132 .9383654 0 3. replace relcommit=relcommit/3(1081 real changes made)(5) Computing the reliability of the index (Cronbach’s alpha). alpha chattend guidance prayer, stdTest scale = mean(standardized items)Average interitem correlation: 0.6177Number of items in the scale: 3Scale reliability coefficient: 0.8290(6) Regression and tolerance statistic with the religious commitment index:. reg bushft partyid ideology educ income south white age sex relcommit Source | SS df MS Number of obs = 800-------------+------------------------------ F( 9, 790) = 120.43 Model | 543820.277 9 60424.4752 Prob > F = 0.0000 Residual | 396357.922 790 501.718888 R-squared = 0.5784-------------+------------------------------ Adj R-squared = 0.5736 Total | 940178.199 799 1176.69362 Root MSE = 22.399------------------------------------------------------------------------------ bushft | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- partyid | 61.75261 2.867855 21.53 0.000 56.12309 67.38213 ideology | 20.58086 4.283983 4.80 0.000 12.17152 28.9902 educ | -12.734 3.340629 -3.81 0.000 -19.29156 -6.176443 income | 3.811059 3.400603 1.12 0.263 -2.864228 10.48635 south | 3.32357 1.754135 1.89 0.058 -.1197466 6.766888 white | -1.576335 2.012684 -0.78 0.434 -5.527177 2.374507 age | 4.823582 3.568376 1.35 0.177 -2.181039 11.8282 sex | .6380074 1.647377 0.39 0.699 -2.595746 3.871761 relcommit | 5.65209 2.844447 1.99 0.047 .0685213 11.23566 _cons | 12.86409 3.430519 3.75 0.000 6.130076 19.5981------------------------------------------------------------------------------. vif Variable | VIF 1/VIF -------------+---------------------- ideology | 1.80 0.556467 partyid | 1.66 0.602932 income | 1.29 0.776917 relcommit | 1.26 0.791065 educ | 1.23 0.809810 white | 1.21 0.825692 sex | 1.08 0.924575 age | 1.08 0.925862 south | 1.07 0.930952-------------+---------------------- Mean VIF |