Some simple models of US county voting outcomes
Some simple models of US county voting outcomes
Woodley convinced me that these are of actual interest. As some of you may recall, I compiled a large county level (n≈3000) dataset some time ago, but didn't use it for anything. I just thought it would be a cool dataset, but that results were not too interesting. Well, since someone did think these were important analyses enough to do a study using state level data on, I took a look at the superior dataset. The outcome variables are the fractions of votes for Democrats, Republicans as well as Libertarians and Greens for the 2016 election. Results for Dems and Reps are also available for 2012 and 2008. The 2016 data also has the various smaller candidates (e.g. this guy) but these were of little interest so I did not examine them.
Data sources
The cognitive ability (CA) score is from what used to be called the Global Report Card but which changed name to (mumble mumble), but one can find them here. I think these are actually from NAEP testing, but I'm not quite sure. They are some kind of scholastic testing, so not exactly standard IQ data, but good enough. The S -- general socioeconomic factor (a fancy general social status metric) -- is extracted from some varied 28 indicators, as detailed in this study. The voter outcome data comes from NYT's map here. It took a bit of a scrape job to get them out, but I managed. The data are actually not the final counts, as I thought they were when I downloaded them, but they are very close to the finals, and so I didn't bother updating them. I guess I should now that someone wants to publish this in some journal with my name on it! Demographic data was from the ACS.
Regressions
While one should use path models, I know that some will want to see the straight regressions. Regressions are basically path models where all the predictors are modeled as being causally independent and which cause the dependent outcome. Thus, one assumes that S is not caused by CA or by demographics. What this basically does is underestimate the variables which mainly work thru other variables (indirect effects).
What am I reporting? I report the standardized betas for the predictors, some model meta-data including cross-validated R2 (10 fold), and the etas. What are etas? These are the square root of the more common eta2., It's an R2-type measure, i.e. about variance, so it is non-linear and not so easy to interpret correctly. Taking the square root puts it on the same scale as the correlation. The etas here are derived from the analysis of variance fit by stats::aov, which is passed to lsr::etaSquared function. This uses type 2 errors by default and I too like to live dangerously so I didn't check method variance by trying the other methods. If you wonder what these are, you can find them explained here, here and here.
Etas have an advantage in comparison to the standardized betas which is that they make it possible to compare the importance of variables for the model's overall explanatory power. Standardized betas do not allow for this because while they are standardized, a variable may be highly correlated with other variables such that it is redundant. Categorical variables may not have much variation. Being a type B may be associated with a large negative effect for some outcome, but if the dataset consists of 99% type A's and 1% type B's, variation in type will not explain much variation in the outcome. Etas take this into account.
Furthermore, categorical variables, such as state, are given a beta for n-1 of their levels (the last level is the reference level and thus has beta=0 using standard contrast coding). So if we have two categorical predictors, one with 5 levels and one with 10, we get a set of 4 betas vs. a set of 9 betas. This makes it hard to assess the relative importance of a categorical predictor compared to ... any other predictor. Etas deal away with this problem because each categorical predictor is only assigned 1 eta value, just as every other variable is.
A problem with etas is that they are directionless (because based on eta2). However, we can look up the direction for the non-categorical variables using the betas. The categorical predictors of course do not have any consistent directions.
Choosing metrics for relative comparison of predictors is actually very difficult and I only used a simple method here because this is the only method I have implemented in my model summary function so far. I should implement the functions from the relaimpo package, but alas, I don't have infinite time. So for now we will pretend that etas are totally fine for this purpose.
Here's the results (6 long tables of numbers):
Democrats, 2016 Model coefficients Estimate Std. Error CI.lower CI.upper CA -0.0934 0.017 -0.127 -0.060 S 0.1281 0.019 0.092 0.164 Black 0.7662 0.017 0.733 0.800 Asian 0.2719 0.012 0.248 0.296 Hispanic 0.3831 0.015 0.354 0.412 State: Alabama 0.0000 NA NA NA State: Arizona 1.1032 0.165 0.779 1.427 State: Arkansas 0.4404 0.091 0.263 0.618 State: California 0.7013 0.107 0.491 0.912 State: Colorado 1.0043 0.101 0.807 1.202 State: Connecticut 1.6893 0.202 1.293 2.085 State: Delaware 1.0288 0.314 0.413 1.645 State: Florida 0.5031 0.095 0.318 0.689 State: Georgia -0.0547 0.078 -0.208 0.099 State: Idaho 0.3316 0.108 0.121 0.543 State: Illinois 0.9745 0.088 0.802 1.147 State: Indiana 0.9326 0.090 0.756 1.109 State: Iowa 1.2884 0.090 1.113 1.464 State: Kansas 0.3538 0.089 0.180 0.528 State: Kentucky 0.7534 0.086 0.584 0.923 State: Louisiana -0.1778 0.093 -0.361 0.005 State: Maine 2.1385 0.150 1.843 2.434 State: Maryland 0.8010 0.130 0.547 1.055 State: Massachusetts 2.5254 0.161 2.211 2.840 State: Michigan 1.3539 0.091 1.175 1.532 State: Minnesota 1.3040 0.092 1.123 1.485 State: Mississippi -0.0042 0.089 -0.178 0.170 State: Missouri 0.6297 0.086 0.462 0.798 State: Montana 1.0762 0.102 0.876 1.277 State: Nebraska 0.3433 0.092 0.162 0.524 State: Nevada 0.2345 0.147 -0.054 0.523 State: New Hampshire 2.1916 0.183 1.833 2.550 State: New Jersey 0.8934 0.145 0.609 1.178 State: New Mexico 0.5739 0.125 0.328 0.820 State: New York 1.3975 0.098 1.205 1.590 State: North Carolina 0.7083 0.086 0.540 0.877 State: North Dakota 0.8483 0.104 0.644 1.053 State: Ohio 1.1032 0.092 0.924 1.283 State: Oklahoma 0.2687 0.092 0.088 0.449 State: Oregon 1.2490 0.115 1.024 1.474 State: Pennsylvania 1.1244 0.096 0.936 1.313 State: Rhode Island 2.2675 0.248 1.780 2.755 State: South Carolina 0.2430 0.102 0.043 0.443 State: South Dakota 1.0742 0.098 0.881 1.267 State: Tennessee 0.4817 0.087 0.310 0.653 State: Texas -0.2096 0.085 -0.376 -0.044 State: Utah 0.2185 0.123 -0.022 0.459 State: Vermont 2.9258 0.159 2.613 3.238 State: Virginia 0.7378 0.083 0.576 0.900 State: Washington 1.3852 0.111 1.167 1.604 State: West Virginia 0.6874 0.100 0.491 0.884 State: Wisconsin 1.7170 0.095 1.530 1.904 State: Wyoming 0.2856 0.132 0.026 0.545
Model meta-data
outcome N R2 R2-adj. R2-cv
1 dem16_frac 3062 0.72 0.72 0.71
Etas from analysis of variance
eta eta.part
CA 0.052 0.098
S 0.066 0.125
Black 0.429 0.632
Asian 0.216 0.380
Hispanic 0.247 0.424
State 0.474 0.670Republicans, 2016 Model coefficients Estimate Std. Error CI.lower CI.upper CA 0.101 0.018 0.065 0.14 S -0.172 0.019 -0.210 -0.13 Black -0.746 0.018 -0.781 -0.71 Asian -0.272 0.013 -0.297 -0.25 Hispanic -0.386 0.016 -0.416 -0.36 State: Alabama 0.000 NA NA NA State: Arizona -1.253 0.173 -1.592 -0.91 State: Arkansas -0.621 0.095 -0.806 -0.44 State: California -0.845 0.112 -1.065 -0.62 State: Colorado -1.264 0.105 -1.471 -1.06 State: Connecticut -1.754 0.211 -2.167 -1.34 State: Delaware -1.136 0.328 -1.779 -0.49 State: Florida -0.531 0.099 -0.725 -0.34 State: Georgia 0.039 0.082 -0.122 0.20 State: Idaho -0.940 0.112 -1.160 -0.72 State: Illinois -1.113 0.092 -1.293 -0.93 State: Indiana -1.052 0.094 -1.236 -0.87 State: Iowa -1.409 0.094 -1.592 -1.23 State: Kansas -0.523 0.093 -0.705 -0.34 State: Kentucky -0.859 0.090 -1.036 -0.68 State: Louisiana 0.118 0.097 -0.073 0.31 State: Maine -2.384 0.157 -2.692 -2.08 State: Maryland -0.873 0.135 -1.138 -0.61 State: Massachusetts -2.649 0.168 -2.978 -2.32 State: Michigan -1.504 0.095 -1.690 -1.32 State: Minnesota -1.554 0.096 -1.743 -1.37 State: Mississippi -0.013 0.093 -0.194 0.17 State: Missouri -0.726 0.090 -0.902 -0.55 State: Montana -1.299 0.107 -1.508 -1.09 State: Nebraska -0.445 0.096 -0.634 -0.26 State: Nevada -0.537 0.154 -0.839 -0.24 State: New Hampshire -2.275 0.191 -2.650 -1.90 State: New Jersey -0.878 0.152 -1.175 -0.58 State: New Mexico -1.087 0.131 -1.343 -0.83 State: New York -1.516 0.103 -1.717 -1.32 State: North Carolina -0.712 0.090 -0.888 -0.54 State: North Dakota -1.111 0.109 -1.325 -0.90 State: Ohio -1.207 0.096 -1.395 -1.02 State: Oklahoma -0.406 0.096 -0.594 -0.22 State: Oregon -1.500 0.120 -1.735 -1.27 State: Pennsylvania -1.159 0.101 -1.357 -0.96 State: Rhode Island -2.342 0.259 -2.851 -1.83 State: South Carolina -0.334 0.107 -0.543 -0.12 State: South Dakota -1.256 0.103 -1.457 -1.05 State: Tennessee -0.538 0.091 -0.717 -0.36 State: Texas 0.189 0.088 0.016 0.36 State: Utah -1.243 0.128 -1.493 -0.99 State: Vermont -3.081 0.166 -3.407 -2.75 State: Virginia -0.840 0.086 -1.010 -0.67 State: Washington -1.572 0.116 -1.800 -1.34 State: West Virginia -0.822 0.105 -1.028 -0.62 State: Wisconsin -1.806 0.099 -2.001 -1.61 State: Wyoming -0.525 0.138 -0.796 -0.25
Model meta-data
outcome N R2 R2-adj. R2-cv
1 rep16_frac 3062 0.7 0.69 0.68
Etas from analysis of variance
eta eta.part
CA 0.056 0.10
S 0.089 0.16
Black 0.418 0.61
Asian 0.216 0.37
Hispanic 0.248 0.41
State 0.496 0.67Greens, 2016 Model coefficients Estimate Std. Error CI.lower CI.upper CA -0.150 0.025 -0.198 -0.101 S 0.076 0.027 0.023 0.128 Black -0.093 0.024 -0.140 -0.045 Asian 0.097 0.017 0.063 0.131 Hispanic -0.030 0.021 -0.072 0.012 State: Alabama 0.000 NA NA NA State: Arizona 1.561 0.215 1.139 1.983 State: Arkansas 0.542 0.118 0.310 0.773 State: California 1.970 0.142 1.691 2.248 State: Colorado 1.466 0.133 1.206 1.726 State: Connecticut 1.942 0.263 1.426 2.458 State: Delaware 1.605 0.407 0.806 2.404 State: Florida 0.399 0.124 0.157 0.642 State: Idaho 0.990 0.141 0.712 1.267 State: Illinois 1.163 0.116 0.936 1.390 State: Iowa 0.403 0.118 0.171 0.635 State: Kansas 2.333 0.117 2.103 2.563 State: Kentucky 0.362 0.114 0.138 0.586 State: Louisiana 0.273 0.121 0.036 0.510 State: Maine 2.606 0.196 2.221 2.991 State: Maryland 1.284 0.169 0.952 1.615 State: Massachusetts 2.365 0.210 1.954 2.777 State: Michigan 1.129 0.120 0.895 1.364 State: Minnesota 1.077 0.122 0.837 1.316 State: Mississippi -0.045 0.115 -0.271 0.181 State: Missouri 0.475 0.113 0.253 0.696 State: Montana 1.407 0.135 1.143 1.671 State: Nebraska 0.603 0.122 0.363 0.842 State: New Hampshire 0.944 0.239 0.477 1.412 State: New Jersey 0.895 0.190 0.522 1.268 State: New Mexico 1.037 0.164 0.715 1.359 State: New York 2.048 0.129 1.795 2.301 State: North Dakota 1.145 0.137 0.876 1.415 State: Ohio 0.700 0.121 0.463 0.937 State: Oregon 2.651 0.150 2.356 2.946 State: Pennsylvania 0.653 0.127 0.405 0.902 State: Rhode Island 1.675 0.323 1.041 2.308 State: South Carolina 0.301 0.133 0.041 0.560 State: Tennessee 0.200 0.115 -0.025 0.424 State: Texas 0.299 0.112 0.079 0.519 State: Utah 0.267 0.161 -0.048 0.582 State: Vermont 2.966 0.208 2.558 3.374 State: Virginia 0.475 0.108 0.264 0.687 State: Washington 1.454 0.146 1.167 1.740 State: West Virginia 1.012 0.132 0.753 1.271 State: Wisconsin 1.021 0.126 0.775 1.267 State: Wyoming 0.868 0.173 0.529 1.208
Model meta-data
outcome N R2 R2-adj. R2-cv
1 green16_frac 2556 0.54 0.53 0.54
Etas from analysis of variance
eta eta.part
CA 0.082 0.119
S 0.039 0.057
Black 0.052 0.076
Asian 0.077 0.112
Hispanic 0.019 0.028
State 0.591 0.655Libertarians, 2016 Model coefficients Estimate Std. Error CI.lower CI.upper CA -0.0038 0.017 -0.0373 0.0296 S 0.3505 0.018 0.3146 0.3865 Black -0.0317 0.017 -0.0648 0.0015 Asian 0.0143 0.012 -0.0091 0.0377 Hispanic 0.0738 0.015 0.0449 0.1026 State: Alabama 0.0000 NA NA NA State: Arizona 1.2045 0.163 0.8846 1.5244 State: Arkansas 0.2946 0.089 0.1192 0.4700 State: California 0.6799 0.106 0.4719 0.8880 State: Colorado 1.0910 0.099 0.8962 1.2858 State: Connecticut 0.3227 0.199 -0.0684 0.7138 State: Delaware 0.7064 0.310 0.0984 1.3144 State: Florida 0.0761 0.093 -0.1071 0.2593 State: Georgia 0.3307 0.077 0.1789 0.4826 State: Idaho 0.6224 0.106 0.4142 0.8307 State: Illinois 1.2047 0.087 1.0347 1.3748 State: Indiana 1.6818 0.089 1.5075 1.8561 State: Iowa 0.4954 0.088 0.3221 0.6687 State: Kansas 0.9395 0.088 0.7679 1.1111 State: Kentucky 0.4006 0.085 0.2331 0.5680 State: Louisiana -0.0810 0.092 -0.2614 0.0995 State: Maine 1.9222 0.149 1.6309 2.2136 State: Maryland 0.4547 0.128 0.2039 0.7056 State: Massachusetts 0.8918 0.159 0.5809 1.2028 State: Michigan 1.0787 0.090 0.9024 1.2549 State: Minnesota 0.7014 0.091 0.5227 0.8801 State: Mississippi -0.1593 0.088 -0.3309 0.0123 State: Missouri 0.6371 0.085 0.4711 0.8032 State: Montana 1.7722 0.101 1.5742 1.9703 State: Nebraska 0.9864 0.091 0.8076 1.1652 State: Nevada 0.8487 0.145 0.5635 1.1339 State: New Hampshire 0.9316 0.181 0.5773 1.2860 State: New Jersey -0.4833 0.143 -0.7645 -0.2021 State: New Mexico 4.4179 0.124 4.1754 4.6604 State: New York 0.7390 0.097 0.5490 0.9291 State: North Carolina 0.3557 0.085 0.1894 0.5220 State: North Dakota 2.0401 0.103 1.8380 2.2422 State: Ohio 0.6618 0.090 0.4846 0.8391 State: Oklahoma 1.7475 0.091 1.5691 1.9259 State: Oregon 1.8205 0.113 1.5986 2.0424 State: Pennsylvania 0.0888 0.095 -0.0976 0.2753 State: Rhode Island 0.5527 0.245 0.0718 1.0336 State: South Carolina 0.1063 0.101 -0.0913 0.3040 State: South Dakota 1.6102 0.097 1.4197 1.8008 State: Tennessee 0.2270 0.086 0.0577 0.3964 State: Texas 0.1331 0.084 -0.0307 0.2970 State: Utah -0.0389 0.121 -0.2762 0.1983 State: Vermont 0.6762 0.157 0.3676 0.9847 State: Virginia 0.3101 0.082 0.1500 0.4701 State: Washington 1.1375 0.110 0.9218 1.3532 State: West Virginia 0.7544 0.099 0.5600 0.9488 State: Wisconsin 0.5313 0.094 0.3471 0.7155 State: Wyoming 1.5085 0.131 1.2524 1.7645
Model meta-data
outcome N R2 R2-adj. R2-cv
1 libert16_frac 3062 0.73 0.73 0.72Etas from analysis of variance
eta eta.part
CA 0.0021 0.0041
S 0.1810 0.3291
Black 0.0177 0.0341
Asian 0.0114 0.0219
Hispanic 0.0475 0.0910
State 0.6146 0.7637Democrats, 2012 Model coefficients Estimate Std. Error CI.lower CI.upper CA -0.136 0.018 -0.172 -0.099 S -0.026 0.020 -0.065 0.013 Black 0.646 0.018 0.611 0.682 Asian 0.210 0.013 0.185 0.236 Hispanic 0.319 0.016 0.288 0.350 State: Alabama 0.000 NA NA NA State: Arizona 0.959 0.177 0.612 1.306 State: Arkansas 0.376 0.097 0.186 0.566 State: California 0.845 0.115 0.620 1.071 State: Colorado 1.324 0.108 1.113 1.534 State: Connecticut 2.204 0.216 1.781 2.628 State: Delaware 1.401 0.336 0.742 2.059 State: Florida 0.604 0.101 0.406 0.803 State: Georgia -0.057 0.084 -0.221 0.108 State: Idaho 0.488 0.115 0.262 0.714 State: Illinois 1.424 0.094 1.240 1.608 State: Indiana 1.322 0.096 1.134 1.511 State: Iowa 2.040 0.096 1.853 2.228 State: Kansas 0.448 0.095 0.263 0.634 State: Kentucky 0.844 0.093 0.662 1.025 State: Louisiana -0.248 0.100 -0.444 -0.053 State: Maine 2.602 0.161 2.286 2.918 State: Maryland 1.135 0.139 0.863 1.407 State: Massachusetts 2.750 0.172 2.413 3.087 State: Michigan 1.806 0.097 1.615 1.997 State: Minnesota 2.026 0.099 1.833 2.220 State: Mississippi -0.059 0.095 -0.244 0.127 State: Missouri 0.973 0.092 0.793 1.152 State: Montana 1.290 0.109 1.075 1.504 State: Nebraska 0.644 0.099 0.451 0.838 State: Nevada 0.517 0.158 0.208 0.826 State: New Hampshire 2.567 0.196 2.183 2.951 State: New Jersey 1.401 0.155 1.097 1.706 State: New Mexico 0.835 0.134 0.572 1.097 State: New York 1.946 0.105 1.740 2.152 State: North Carolina 0.790 0.092 0.610 0.970 State: North Dakota 1.439 0.112 1.220 1.658 State: Ohio 1.662 0.098 1.470 1.854 State: Oklahoma 0.369 0.099 0.175 0.562 State: Oregon 1.403 0.123 1.163 1.644 State: Pennsylvania 1.479 0.103 1.277 1.681 State: Rhode Island 2.731 0.266 2.210 3.252 State: South Carolina 0.320 0.109 0.106 0.534 State: South Dakota 1.538 0.105 1.332 1.743 State: Tennessee 0.603 0.094 0.420 0.787 State: Texas -0.236 0.091 -0.413 -0.058 State: Utah 0.032 0.131 -0.225 0.289 State: Vermont 3.380 0.170 3.046 3.714 State: Virginia 0.967 0.088 0.794 1.141 State: Washington 1.511 0.119 1.278 1.745 State: West Virginia 0.928 0.107 0.718 1.139 State: Wisconsin 2.270 0.102 2.070 2.469 State: Wyoming 0.439 0.141 0.162 0.717
Model meta-data
outcome N R2 R2-adj. R2-cv
1 dem12_frac 3063 0.68 0.68 0.67
Etas from analysis of variance
eta eta.part
CA 0.075 0.132
S 0.013 0.024
Black 0.363 0.542
Asian 0.167 0.285
Hispanic 0.205 0.343
State 0.619 0.740Republicans 2012 Model coefficients Estimate Std. Error CI.lower CI.upper CA 0.138 0.019 0.102 0.175 S 0.026 0.020 -0.013 0.066 Black -0.624 0.019 -0.661 -0.588 Asian -0.211 0.013 -0.237 -0.185 Hispanic -0.310 0.016 -0.341 -0.278 State: Alabama 0.000 NA NA NA State: Arizona -1.016 0.179 -1.367 -0.665 State: Arkansas -0.481 0.098 -0.674 -0.288 State: California -0.973 0.117 -1.201 -0.744 State: Colorado -1.411 0.109 -1.625 -1.197 State: Connecticut -2.210 0.219 -2.640 -1.781 State: Delaware -1.425 0.341 -2.092 -0.757 State: Florida -0.596 0.103 -0.797 -0.395 State: Georgia 0.047 0.085 -0.120 0.214 State: Idaho -0.582 0.117 -0.810 -0.353 State: Illinois -1.469 0.095 -1.656 -1.282 State: Indiana -1.378 0.098 -1.569 -1.187 State: Iowa -2.066 0.097 -2.256 -1.875 State: Kansas -0.506 0.096 -0.695 -0.318 State: Kentucky -0.859 0.094 -1.043 -0.676 State: Louisiana 0.208 0.101 0.010 0.406 State: Maine -2.698 0.163 -3.018 -2.378 State: Maryland -1.211 0.140 -1.486 -0.935 State: Massachusetts -2.796 0.174 -3.137 -2.455 State: Michigan -1.792 0.099 -1.986 -1.599 State: Minnesota -2.093 0.100 -2.290 -1.897 State: Mississippi 0.047 0.096 -0.142 0.235 State: Missouri -1.027 0.093 -1.210 -0.845 State: Montana -1.390 0.111 -1.608 -1.173 State: Nebraska -0.696 0.100 -0.893 -0.500 State: Nevada -0.643 0.160 -0.957 -0.330 State: New Hampshire -2.579 0.198 -2.968 -2.190 State: New Jersey -1.419 0.157 -1.728 -1.111 State: New Mexico -1.009 0.136 -1.275 -0.743 State: New York -1.987 0.106 -2.196 -1.779 State: North Carolina -0.804 0.093 -0.987 -0.622 State: North Dakota -1.529 0.113 -1.751 -1.307 State: Ohio -1.717 0.099 -1.912 -1.523 State: Oklahoma -0.272 0.100 -0.468 -0.076 State: Oregon -1.559 0.124 -1.803 -1.315 State: Pennsylvania -1.482 0.104 -1.687 -1.277 State: Rhode Island -2.780 0.269 -3.308 -2.252 State: South Carolina -0.346 0.111 -0.563 -0.129 State: South Dakota -1.584 0.106 -1.792 -1.376 State: Tennessee -0.612 0.095 -0.798 -0.426 State: Texas 0.228 0.092 0.048 0.408 State: Utah -0.084 0.133 -0.345 0.176 State: Vermont -3.447 0.173 -3.786 -3.108 State: Virginia -1.010 0.090 -1.185 -0.834 State: Washington -1.601 0.121 -1.838 -1.364 State: West Virginia -0.989 0.109 -1.202 -0.775 State: Wisconsin -2.262 0.103 -2.464 -2.059 State: Wyoming -0.581 0.143 -0.862 -0.300
Model meta-data
outcome N R2 R2-adj. R2-cv
1 rep12_frac 3063 0.67 0.67 0.66
Etas from analysis of variance
eta eta.part
CA 0.077 0.133
S 0.014 0.024
Black 0.350 0.523
Asian 0.168 0.282
Hispanic 0.200 0.330
State 0.626 0.739Democrats, 2008 Model coefficients Estimate Std. Error CI.lower CI.upper CA -0.118 0.020 -0.156 -0.0793 S -0.045 0.021 -0.086 -0.0038 Black 0.609 0.019 0.571 0.6470 Asian 0.215 0.014 0.188 0.2415 Hispanic 0.280 0.017 0.247 0.3131 State: Alabama 0.000 NA NA NA State: Arizona 1.005 0.187 0.639 1.3719 State: Arkansas 0.477 0.103 0.276 0.6776 State: California 1.054 0.122 0.815 1.2922 State: Colorado 1.512 0.114 1.289 1.7349 State: Connecticut 2.444 0.229 1.996 2.8920 State: Delaware 1.666 0.355 0.969 2.3626 State: Florida 0.700 0.107 0.491 0.9104 State: Georgia 0.014 0.089 -0.160 0.1883 State: Idaho 0.626 0.122 0.388 0.8650 State: Illinois 1.867 0.099 1.672 2.0617 State: Indiana 1.758 0.102 1.558 1.9573 State: Iowa 2.236 0.101 2.038 2.4347 State: Kansas 0.592 0.100 0.395 0.7887 State: Kentucky 1.068 0.098 0.876 1.2600 State: Louisiana -0.253 0.105 -0.460 -0.0461 State: Maine 2.698 0.170 2.364 3.0317 State: Maryland 1.211 0.147 0.924 1.4988 State: Massachusetts 2.916 0.182 2.559 3.2718 State: Michigan 2.100 0.103 1.898 2.3017 State: Minnesota 2.170 0.104 1.966 2.3752 State: Mississippi -0.057 0.100 -0.253 0.1401 State: Missouri 1.308 0.097 1.117 1.4978 State: Montana 1.603 0.116 1.376 1.8296 State: Nebraska 0.800 0.104 0.595 1.0050 State: Nevada 0.809 0.167 0.482 1.1356 State: New Hampshire 2.730 0.207 2.324 3.1360 State: New Jersey 1.424 0.164 1.102 1.7461 State: New Mexico 1.208 0.142 0.930 1.4857 State: New York 1.978 0.111 1.760 2.1954 State: North Carolina 0.923 0.097 0.732 1.1133 State: North Dakota 1.820 0.118 1.588 2.0512 State: Ohio 1.728 0.104 1.525 1.9308 State: Oklahoma 0.369 0.104 0.165 0.5737 State: Oregon 1.610 0.130 1.356 1.8644 State: Pennsylvania 1.727 0.109 1.513 1.9406 State: Rhode Island 2.849 0.281 2.298 3.3999 State: South Carolina 0.396 0.115 0.170 0.6227 State: South Dakota 1.819 0.111 1.602 2.0364 State: Tennessee 0.765 0.099 0.571 0.9589 State: Texas -0.020 0.096 -0.208 0.1673 State: Utah 0.510 0.139 0.238 0.7816 State: Vermont 3.485 0.180 3.132 3.8387 State: Virginia 1.154 0.094 0.971 1.3373 State: Washington 1.662 0.126 1.415 1.9092 State: West Virginia 1.408 0.114 1.185 1.6309 State: Wisconsin 2.585 0.108 2.374 2.7964 State: Wyoming 0.669 0.150 0.375 0.9618
Model meta-data
outcome N R2 R2-adj. R2-cv
1 dem08_frac 3063 0.65 0.64 0.63
Etas from analysis of variance
eta eta.part
CA 0.065 0.109
S 0.023 0.039
Black 0.342 0.498
Asian 0.171 0.276
Hispanic 0.180 0.290
State 0.650 0.738Republicans, 2008 Model coefficients Estimate Std. Error CI.lower CI.upper CA 0.118 0.020 0.0795 0.157 S 0.055 0.021 0.0137 0.096 Black -0.586 0.019 -0.6237 -0.548 Asian -0.213 0.014 -0.2394 -0.186 Hispanic -0.269 0.017 -0.3026 -0.236 State: Alabama 0.000 NA NA NA State: Arizona -1.026 0.188 -1.3945 -0.658 State: Arkansas -0.612 0.103 -0.8139 -0.410 State: California -1.160 0.122 -1.3994 -0.920 State: Colorado -1.571 0.114 -1.7953 -1.347 State: Connecticut -2.479 0.230 -2.9297 -2.029 State: Delaware -1.684 0.357 -2.3848 -0.984 State: Florida -0.698 0.108 -0.9085 -0.486 State: Georgia -0.012 0.089 -0.1866 0.163 State: Idaho -0.725 0.122 -0.9651 -0.485 State: Illinois -1.905 0.100 -2.1011 -1.709 State: Indiana -1.771 0.102 -1.9721 -1.571 State: Iowa -2.277 0.102 -2.4770 -2.078 State: Kansas -0.638 0.101 -0.8356 -0.440 State: Kentucky -1.087 0.098 -1.2802 -0.894 State: Louisiana 0.201 0.106 -0.0064 0.409 State: Maine -2.753 0.171 -3.0890 -2.418 State: Maryland -1.276 0.147 -1.5644 -0.987 State: Massachusetts -3.008 0.183 -3.3657 -2.649 State: Michigan -2.146 0.104 -2.3493 -1.943 State: Minnesota -2.269 0.105 -2.4747 -2.063 State: Mississippi 0.046 0.101 -0.1518 0.244 State: Missouri -1.342 0.098 -1.5336 -1.151 State: Montana -1.760 0.116 -1.9885 -1.532 State: Nebraska -0.861 0.105 -1.0665 -0.655 State: Nevada -0.984 0.168 -1.3127 -0.656 State: New Hampshire -2.747 0.208 -3.1548 -2.339 State: New Jersey -1.454 0.165 -1.7781 -1.130 State: New Mexico -1.242 0.142 -1.5216 -0.963 State: New York -2.012 0.112 -2.2308 -1.793 State: North Carolina -0.927 0.098 -1.1188 -0.736 State: North Dakota -1.899 0.119 -2.1321 -1.666 State: Ohio -1.786 0.104 -1.9901 -1.582 State: Oklahoma -0.273 0.105 -0.4785 -0.067 State: Oregon -1.750 0.130 -2.0059 -1.495 State: Pennsylvania -1.746 0.110 -1.9607 -1.531 State: Rhode Island -2.922 0.283 -3.4759 -2.368 State: South Carolina -0.429 0.116 -0.6565 -0.201 State: South Dakota -1.893 0.111 -2.1112 -1.674 State: Tennessee -0.788 0.099 -0.9826 -0.593 State: Texas 0.027 0.096 -0.1613 0.216 State: Utah -0.652 0.139 -0.9248 -0.378 State: Vermont -3.556 0.181 -3.9110 -3.200 State: Virginia -1.176 0.094 -1.3603 -0.992 State: Washington -1.738 0.127 -1.9868 -1.490 State: West Virginia -1.450 0.114 -1.6740 -1.226 State: Wisconsin -2.613 0.108 -2.8253 -2.401 State: Wyoming -0.781 0.150 -1.0759 -0.486
Model meta-data
outcome N R2 R2-adj. R2-cv
1 rep08_frac 3063 0.64 0.64 0.63
Etas from analysis of variance
eta eta.part
CA 0.065 0.109
S 0.028 0.047
Black 0.329 0.482
Asian 0.169 0.272
Hispanic 0.174 0.279
State 0.661 0.741Summary & interpretation
In general, the models performed fairly well, the mean cross-validated R2 was 65% (54% to 72%). The best way to summarize the findings for the predictors would be to aggregate/meta-analyze the results. I'm too busy to do that now, so we will just look at the non-state predictors presented in less space:
CA S Black Asian Hispanic group
1 -0.09 0.13 0.77 0.27 0.38 fit_dem16
2 0.10 -0.17 -0.75 -0.27 -0.39 fit_rep16
3 -0.15 0.08 -0.09 0.10 -0.03 fit_green16
4 0.00 0.35 -0.03 0.01 0.07 fit_liber16
5 -0.14 -0.03 0.65 0.21 0.32 fit_dem12
6 0.14 0.03 -0.62 -0.21 -0.31 fit_rep12
7 -0.12 -0.04 0.61 0.21 0.28 fit_dem08
8 0.12 0.06 -0.59 -0.21 -0.27 fit_rep08So, for predicting democrat votes, we can see that the betas are all negative for CA: -.09, -.14 and -.12. All else equal, smarter counties voted less for democrats, whether it was Clinton or Obama. S is weird. The beta for 2016 was .13 but it was -.03 and -.04 for 2012 and 2008! A sign change and it's not a chance finding because the use of a dataset with n≈3,000 gives us a lot of precision, and none of these did actually have CIs that even overlapped zero. So for 2016 this gives us the odd situation where the highly correlated CA and S variables (r = .71) have reverse signs for the outcome: -.09 and .13. Smarter counties voted less for democrats, but those higher in S voted more for democrats -- all else equal. That wasn't so in the Obama elections where CA and S had the same directions. As for demographics, the situation is not surprising: non-Whites like democrats, a lot. We knew this from simpler statistics showing that Blacks vote 93% for Obama. The curious finding here is that this was not just due to the lower CA and S for Blacks or Hispanics. The Black effect was even stronger for the 2016 election than the Obama ones, which is somewhat curious. The general idea seems to be that minorities like to vote for their own candidates, but it seems not to be the case for these data. Or there's some annoying confound, like turnout %. Hispanics are voting increasingly for democrats (betas: .28 to .32 to .38) and Asians too, maybe (.21 to .21 to .27). The republican results are not so interesting because they are essentially the opposite of the democrat results (for non-2016, they are necessarily the opposite because NYT did away with the third party votes).
Results for the two smaller parties are somewhat interesting. Greens showed the same mismatch in directionality for CA and S, just with reversed beta strengths (-.15 and .08; CA stronger, reverse for democrats). Interestingly for libertarians, there was no effect of CA, but a large one of S (.35). Given the generally positive correlations between libertarian preferences and CA, this is somewhat surprising (see this and this). Perhaps more interestingly, demographics had little to no effect on preferences for libertarians. This was also true to a bit lesser extent for greens.
The relative importance of variables can be glanced from the etas. Most of the models' validity is due to state-level effects (whatever these represent) and demographics, mostly % Blacks. The mean eta for State was .59 (range: .47 to .66), and for Black .29 (.02 to .43). The small values for Black are from the third parties which, as we saw, were not a thing that Blacks cared much about as a group once controlled for CA and S. CA and S themselves had mean etas of .06. As such, cognitive ability and social inequality were not particularly important for explaining the election outcomes at the county level.
Other notes:
Analyses were unweighted. I reasoned that we are here thinking of the counties as the units of interest, and so we should weigh them equally, not give more weight to the larger counties. We would do that if we were interested in modeling the national outcome itself or persons inside counties.
For the Green's analysis, n≈2,500. Why is n only about 2,500 instead of 3,000? Because the Greens did not run in all states, and so these have missing data. Perhaps one should impute these values, maybe with 0%, maybe with estimated values.