Negative Binomial model
Appears appropriate to use Negative Binomial Regression, as the conditional variance exceeds the conditional mean (i.e., the mean for each observation is greater than its variance)
State-level
## AZ CA CO CT DC FL GA IL IN LA MA MN MO NC NH NJ NM NY OH OR PA SC TX UT VA WI
## "M (SD) = 33.33 (1221.33)" "M (SD) = 74.33 (5332.27)" "M (SD) = 40.00 (NA)" "M (SD) = 24.67 (552.33)" "M (SD) = 33.00 (NA)" "M (SD) = 6.75 (10.92)" "M (SD) = 22.00 (72.00)" "M (SD) = 35.00 (2178.00)" "M (SD) = 28.50 (60.50)" "M (SD) = 10.00 (32.00)" "M (SD) = 89.25 (3056.92)" "M (SD) = 9.00 (NA)" "M (SD) = 100.00 (NA)" "M (SD) = 3.50 (12.50)" "M (SD) = 51.00 (3042.00)" "M (SD) = 7.50 (60.50)" "M (SD) = 16.00 (NA)" "M (SD) = 72.50 (8710.29)" "M (SD) = 19.00 (578.00)" "M (SD) = 30.00 (NA)" "M (SD) = 17.50 (480.50)" "M (SD) = 2.00 (NA)" "M (SD) = 39.25 (1182.92)" "M (SD) = 19.00 (NA)" "M (SD) = 33.50 (1092.33)" "M (SD) = 34.00 (NA)"Cong-Dist level
## AZ-02 AZ-04 AZ-07 CA-2 CA-36 CA-37 CA-50 CO-1 CT-02 CT-03 DC-AL FL-02 FL-03 FL-15 GA-05 GA-10 IL-13 IL-7 IN-09 LA-01 MA-02 MA-07 MA-7 MN-05 MO-01 NC-04 NC-12 NH-01 NH-02 NJ-12 NM-01 NY-01 NY-10 NY-12 NY-13 NY-15 NY-26 OH-03 OR-01 PA-03 PA-12 SC-06 TX-18 TX-32 TX-37 UT-01 VA-04 VA-05 VA-09 VA-7 WI-02
## "M (SD) = 24.00 (NA)" "M (SD) = 72.00 (NA)" "M (SD) = 4.00 (NA)" "M (SD) = 17.50 (20.51)" "M (SD) = 127.00 (117.38)" "M (SD) = 93.00 (NA)" "M (SD) = 64.00 (NA)" "M (SD) = 40.00 (NA)" "M (SD) = 13.00 (16.97)" "M (SD) = 48.00 (NA)" "M (SD) = 33.00 (NA)" "M (SD) = 5.00 (NA)" "M (SD) = 9.00 (NA)" "M (SD) = 6.50 (4.95)" "M (SD) = 28.00 (NA)" "M (SD) = 16.00 (NA)" "M (SD) = 2.00 (NA)" "M (SD) = 68.00 (NA)" "M (SD) = 28.50 (7.78)" "M (SD) = 10.00 (5.66)" "M (SD) = 132.00 (NA)" "M (SD) = 53.50 (62.93)" "M (SD) = 118.00 (NA)" "M (SD) = 9.00 (NA)" "M (SD) = 100.00 (NA)" "M (SD) = 6.00 (NA)" "M (SD) = 1.00 (NA)" "M (SD) = 12.00 (NA)" "M (SD) = 90.00 (NA)" "M (SD) = 7.50 (7.78)" "M (SD) = 16.00 (NA)" "M (SD) = 29.00 (NA)" "M (SD) = 63.00 (62.45)" "M (SD) = 50.00 (NA)" "M (SD) = 282.00 (NA)" "M (SD) = 15.00 (NA)" "M (SD) = 15.00 (NA)" "M (SD) = 19.00 (24.04)" "M (SD) = 30.00 (NA)" "M (SD) = 33.00 (NA)" "M (SD) = 2.00 (NA)" "M (SD) = 2.00 (NA)" "M (SD) = 2.00 (NA)" "M (SD) = 21.00 (NA)" "M (SD) = 67.00 (16.97)" "M (SD) = 19.00 (NA)" "M (SD) = 13.00 (NA)" "M (SD) = 27.00 (NA)" "M (SD) = 82.00 (NA)" "M (SD) = 12.00 (NA)" "M (SD) = 34.00 (NA)"Analyses
State
##
## Call:
## glm.nb(formula = Arrested ~ allmdpc, data = state_protestschools,
## init.theta = 0.9288757386, link = log)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.469 0.140 24.81 < 0.0000000000000002 ***
## allmdpc 0.392 0.118 3.31 0.00093 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(0.9289) family taken to be 1)
##
## Null deviance: 81.693 on 62 degrees of freedom
## Residual deviance: 71.647 on 61 degrees of freedom
## (1 observation deleted due to missingness)
## AIC: 588.6
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 0.929
## Std. Err.: 0.153
##
## 2 x log-likelihood: -582.643##
## Call:
## glm.nb(formula = Arrested ~ allmdpc + Schoolname, data = state_protestschools,
## init.theta = 7.283030766, link = log)
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 4.340 0.454 9.56 < 0.0000000000000002 ***
## allmdpc 0.453 0.621 0.73 0.46599
## SchoolnameArt Institute of Chicago (school is a couple blocks away) -0.598 1.121 -0.53 0.59372
## SchoolnameCal Poly Humboldt -1.880 1.001 -1.88 0.06047 .
## SchoolnameColumbia University/City College of New York 0.724 1.243 0.58 0.56034
## SchoolnameDartmouth College -0.674 1.576 -0.43 0.66885
## SchoolnameEmerson College -0.527 1.737 -0.30 0.76181
## SchoolnameEmory University -0.631 0.525 -1.20 0.22926
## SchoolnameFashion Institute of Technology -1.006 1.249 -0.81 0.42068
## SchoolnameFlorida State University -2.543 0.652 -3.90 0.0000957 ***
## SchoolnameFordham University -2.210 1.268 -1.74 0.08134 .
## SchoolnameGeorge Washington University -2.138 2.191 -0.98 0.32915
## SchoolnameIndiana University -0.599 0.442 -1.36 0.17507
## SchoolnameMassachusetts Institute of Technology -3.100 1.767 -1.75 0.07928 .
## SchoolnameNew York University -0.628 1.216 -0.52 0.60581
## SchoolnameNortheastern University -0.712 1.738 -0.41 0.68188
## SchoolnameNorthern Arizona University -1.099 0.575 -1.91 0.05588 .
## SchoolnameOhio State University -1.298 0.472 -2.75 0.00597 **
## SchoolnamePortland State University -1.237 0.915 -1.35 0.17650
## SchoolnamePrinceton University -2.764 1.066 -2.59 0.00950 **
## SchoolnameStony Brook University -1.551 1.255 -1.24 0.21665
## SchoolnameThe New School -1.157 1.251 -0.92 0.35497
## SchoolnameThe University of New Mexico -1.866 0.931 -2.00 0.04505 *
## SchoolnameTulane University -1.508 0.575 -2.62 0.00869 **
## SchoolnameUniversity at Buffalo -2.210 1.268 -1.74 0.08134 .
## SchoolnameUniversity of Arizona -2.890 0.734 -3.94 0.0000819 ***
## SchoolnameUniversity of California, Los Angeles 0.102 0.989 0.10 0.91754
## SchoolnameUniversity of California, San Diego -0.583 1.029 -0.57 0.57092
## SchoolnameUniversity of Colorado Denver, Community College of Denver and Metropolitan State University of Denver -0.585 0.558 -1.05 0.29446
## SchoolnameUniversity of Connecticut -1.306 0.515 -2.54 0.01120 *
## SchoolnameUniversity of Florida -1.955 0.580 -3.37 0.00074 ***
## SchoolnameUniversity of Georgia -1.191 0.550 -2.17 0.03033 *
## SchoolnameUniversity of Houston -3.140 0.910 -3.45 0.00056 ***
## SchoolnameUniversity of Illinois, Urbana-Champaign -4.125 1.320 -3.12 0.00178 **
## SchoolnameUniversity of Mary Washington -2.291 1.102 -2.08 0.03756 *
## SchoolnameUniversity of Massachusetts Amherst -0.414 1.737 -0.24 0.81141
## SchoolnameUniversity of Minnesota -2.677 1.231 -2.17 0.02971 *
## SchoolnameUniversity of New Hampshire -2.689 1.599 -1.68 0.09255 .
## SchoolnameUniversity of North Carolina Charlotte -3.857 1.143 -3.37 0.00074 ***
## SchoolnameUniversity of North Carolina-Chapel Hill -2.066 0.688 -3.00 0.00267 **
## SchoolnameUniversity of Pennsylvania -1.192 0.973 -1.23 0.22023
## SchoolnameUniversity of Pittsburgh -3.996 1.190 -3.36 0.00078 ***
## SchoolnameUniversity of South Carolina -2.421 1.569 -1.54 0.12290
## SchoolnameUniversity of South Florida -2.281 0.483 -4.72 0.0000023 ***
## SchoolnameUniversity of Southern California -0.209 1.026 -0.20 0.83846
## SchoolnameUniversity of Texas at Austin 0.372 0.516 0.72 0.47181
## SchoolnameUniversity of Texas at Dallas -0.789 0.613 -1.29 0.19814
## SchoolnameUniversity of Utah -1.749 0.990 -1.77 0.07714 .
## SchoolnameUniversity of Virginia -1.480 1.081 -1.37 0.17068
## SchoolnameUniversity of Wisconsin-Madison -1.240 1.065 -1.16 0.24424
## SchoolnameVirginia Commonwealth University -2.211 1.099 -2.01 0.04418 *
## SchoolnameVirginia Tech -0.369 1.069 -0.35 0.72962
## SchoolnameWashington University 0.484 0.477 1.01 0.31037
## SchoolnameYale University NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(7.283) family taken to be 1)
##
## Null deviance: 491.085 on 62 degrees of freedom
## Residual deviance: 66.252 on 10 degrees of freedom
## (1 observation deleted due to missingness)
## AIC: 571.3
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 7.28
## Std. Err.: 1.86
##
## 2 x log-likelihood: -463.34Congressional District
##
## Call:
## glm.nb(formula = Arrested ~ allmdpc, data = congdist_protestschools,
## init.theta = 0.6829360526, link = log)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.5661 0.2665 13.4 <0.0000000000000002 ***
## allmdpc 0.1686 0.0885 1.9 0.057 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(0.6829) family taken to be 1)
##
## Null deviance: 34.525 on 26 degrees of freedom
## Residual deviance: 31.719 on 25 degrees of freedom
## (37 observations deleted due to missingness)
## AIC: 263.3
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 0.683
## Std. Err.: 0.165
##
## 2 x log-likelihood: -257.275##
## Call:
## glm.nb(formula = Arrested ~ allmdpc + Schoolname, data = congdist_protestschools,
## init.theta = 4.333630797, link = log)
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.553 0.777 3.29 0.0010 **
## allmdpc 0.418 0.258 1.62 0.1045
## SchoolnameCal Poly Humboldt -0.604 0.538 -1.12 0.2617
## SchoolnameColumbia University/City College of New York 2.306 0.638 3.62 0.0003 ***
## SchoolnameEmerson College 0.987 0.612 1.61 0.1067
## SchoolnameFashion Institute of Technology -0.597 0.805 -0.74 0.4588
## SchoolnameFordham University -0.384 0.744 -0.52 0.6057
## SchoolnameNew York University -0.214 0.719 -0.30 0.7662
## SchoolnamePrinceton University -1.780 0.564 -3.15 0.0016 **
## SchoolnameThe New School -0.743 0.806 -0.92 0.3564
## SchoolnameUniversity at Buffalo -0.481 0.718 -0.67 0.5033
## SchoolnameUniversity of California, Los Angeles 2.109 0.762 2.77 0.0056 **
## SchoolnameUniversity of California, San Diego 2.513 1.389 1.81 0.0704 .
## SchoolnameUniversity of Colorado Denver, Community College of Denver and Metropolitan State University of Denver 0.381 0.660 0.58 0.5638
## SchoolnameUniversity of Georgia 2.192 2.011 1.09 0.2756
## SchoolnameUniversity of Houston -0.177 1.958 -0.09 0.9279
## SchoolnameUniversity of Illinois, Urbana-Champaign -0.829 1.615 -0.51 0.6077
## SchoolnameUniversity of Mary Washington -0.230 0.889 -0.26 0.7957
## SchoolnameUniversity of North Carolina Charlotte -2.984 1.241 -2.41 0.0162 *
## SchoolnameUniversity of Pittsburgh -1.826 1.168 -1.56 0.1179
## SchoolnameUniversity of South Florida -0.460 1.001 -0.46 0.6459
## SchoolnameUniversity of Southern California -0.727 1.154 -0.63 0.5287
## SchoolnameUniversity of Texas at Dallas NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(4.334) family taken to be 1)
##
## Null deviance: 184.364 on 26 degrees of freedom
## Residual deviance: 25.844 on 5 degrees of freedom
## (37 observations deleted due to missingness)
## AIC: 251
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 4.33
## Std. Err.: 1.44
##
## 2 x log-likelihood: -204.98