Week IV - Count Data Models
R.H.Lowe Jr., M.S. | March 4, 2019 | DEM 7283 | UTSA College of Public Policy
Research Question
For this assignment, we want to know whether the total number of lifetime sexual partners in Ghana is associated with tribal ethncity, religion, marital status and age.
An offset term is not neccesarily useful here. While it would be interesting to examine sexual partner rates across ethnicity or religion, this particular dataset does not have a denominator (numerator for that matter) to calculate a rate.
library(car)## Loading required package: carDatalibrary(stargazer)##
## Please cite as:## Hlavac, Marek (2018). stargazer: Well-Formatted Regression and Summary Statistics Tables.## R package version 5.2.2. https://CRAN.R-project.org/package=stargazerlibrary(survey)## Loading required package: grid## Loading required package: Matrix## Loading required package: survival##
## Attaching package: 'survey'## The following object is masked from 'package:graphics':
##
## dotchartlibrary(sjPlot)## Install package "strengejacke" from GitHub (`devtools::install_github("strengejacke/strengejacke")`) to load all sj-packages at once!library(ggplot2)
require(dplyr)## Loading required package: dplyr##
## Attaching package: 'dplyr'## The following object is masked from 'package:car':
##
## recode## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionOutcome variable is ‘FG9’:
Q: Total number of living daughters __
library(haven)
wm <- read_sav("Library/Mobile Documents/com~apple~CloudDocs/Desktop/Data/Ghana MICS 2011 SPSS Datasets/wm.sav")
#religion
wm$religion<-Recode(wm$WB8,
recodes="11='Catholic'; 12='Protestant';15='Jehovah Witness';16='Moslem';97='None';else=NA",
as.factor=T)
wm$religion<-relevel(wm$religion, ref='None')
#ethnicity
wm$ethnicity<-Recode(wm$WB9,
recodes="11='Akan'; 12='Ga/Damgme';13='Ewe';14='Guan';15='Gruma';
21='Mole Dagbani'; 22='Grusi';23='Mande'; 24='Non-Ghanaian';else=NA",
as.factor=T)
wm$ethnicity<-relevel(wm$ethnicity, ref='Non-Ghanaian')
#union
wm$mrg<-Recode(wm$MA1,
recodes="1='Marriage'; 2='Cohabiting'; 3='Single'",
as.factor=T)
wm$mrg<-relevel(wm$mrg, ref='Marriage')
#age
wm$agec<-cut(wm$WB2, breaks=c(0,15,25,35,49))
#education level
wm$educ<-Recode(wm$WB4,
recodes="0='Pre'; 1='Prim'; 2='Sec'; 3='High';9=NA",
as.factor=T)
wm$educ<-relevel(wm$educ, ref='Pre')
#literacy
wm$lit<-Recode(wm$WB7,
recodes="1:2='Unread'; 3='Read'; 5='Impaired'; else=NA",
as.factor=T)
wm$lit<-relevel(wm$lit, ref='Read')
#sexual partners (DV)
wm$sexprt<-Recode(wm$SB15,
recodes="20:98=NA")
sub<-wm%>%
dplyr::select(FG9,sexprt,ethnicity,religion,mrg,agec,educ,lit,wmweight, HH1) %>%
filter( complete.cases(.))
#First we tell R our survey design
options(survey.lonely.psu = "adjust")
des<-svydesign(ids=~HH1,weights=~wmweight, data =sub )
hist(wm$sexprt)
summary(wm$sexprt)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 1.000 1.000 2.000 1.911 2.000 19.000 1891Poisson Regression
svyhist(~sexprt, des)
svyby(~sexprt, ~religion+ethnicity, des, svymean, na.rm=T)## religion ethnicity sexprt
## Catholic.Non-Ghanaian Catholic Non-Ghanaian 2.660773
## Moslem.Non-Ghanaian Moslem Non-Ghanaian 2.000000
## Protestant.Non-Ghanaian Protestant Non-Ghanaian 5.000000
## None.Akan None Akan 3.056638
## Catholic.Akan Catholic Akan 2.399840
## Jehovah Witness.Akan Jehovah Witness Akan 2.041084
## Moslem.Akan Moslem Akan 2.210184
## Protestant.Akan Protestant Akan 2.346774
## None.Ewe None Ewe 2.229348
## Catholic.Ewe Catholic Ewe 2.264897
## Jehovah Witness.Ewe Jehovah Witness Ewe 1.641895
## Moslem.Ewe Moslem Ewe 1.957468
## Protestant.Ewe Protestant Ewe 3.088463
## Catholic.Ga/Damgme Catholic Ga/Damgme 2.283754
## Jehovah Witness.Ga/Damgme Jehovah Witness Ga/Damgme 3.845096
## Moslem.Ga/Damgme Moslem Ga/Damgme 1.000000
## Protestant.Ga/Damgme Protestant Ga/Damgme 2.724823
## None.Gruma None Gruma 2.010600
## Catholic.Gruma Catholic Gruma 2.024400
## Moslem.Gruma Moslem Gruma 1.000000
## Protestant.Gruma Protestant Gruma 1.228169
## None.Grusi None Grusi 1.357139
## Catholic.Grusi Catholic Grusi 2.346669
## Moslem.Grusi Moslem Grusi 1.228979
## Protestant.Grusi Protestant Grusi 2.452795
## Catholic.Guan Catholic Guan 2.148941
## Jehovah Witness.Guan Jehovah Witness Guan 3.688369
## Moslem.Guan Moslem Guan 2.854377
## Protestant.Guan Protestant Guan 2.361815
## None.Mande None Mande 1.000000
## Catholic.Mande Catholic Mande 2.000000
## Jehovah Witness.Mande Jehovah Witness Mande 1.000000
## Protestant.Mande Protestant Mande 1.000000
## None.Mole Dagbani None Mole Dagbani 1.311147
## Catholic.Mole Dagbani Catholic Mole Dagbani 1.675174
## Jehovah Witness.Mole Dagbani Jehovah Witness Mole Dagbani 1.890015
## Moslem.Mole Dagbani Moslem Mole Dagbani 1.276653
## Protestant.Mole Dagbani Protestant Mole Dagbani 1.906476
## se
## Catholic.Non-Ghanaian 0.65969047
## Moslem.Non-Ghanaian 0.00000000
## Protestant.Non-Ghanaian 0.00000000
## None.Akan 0.41741913
## Catholic.Akan 0.14216028
## Jehovah Witness.Akan 0.26589278
## Moslem.Akan 0.17377747
## Protestant.Akan 0.07733238
## None.Ewe 0.21090247
## Catholic.Ewe 0.27754352
## Jehovah Witness.Ewe 0.32539919
## Moslem.Ewe 0.37819344
## Protestant.Ewe 0.31866482
## Catholic.Ga/Damgme 0.70981594
## Jehovah Witness.Ga/Damgme 0.69081862
## Moslem.Ga/Damgme 0.00000000
## Protestant.Ga/Damgme 0.25801467
## None.Gruma 0.18823193
## Catholic.Gruma 0.39200194
## Moslem.Gruma 0.00000000
## Protestant.Gruma 0.24446457
## None.Grusi 0.21905485
## Catholic.Grusi 0.48450172
## Moslem.Grusi 0.24992156
## Protestant.Grusi 0.59198421
## Catholic.Guan 0.16235306
## Jehovah Witness.Guan 1.24790801
## Moslem.Guan 0.15816380
## Protestant.Guan 0.36593426
## None.Mande 0.00000000
## Catholic.Mande 0.00000000
## Jehovah Witness.Mande 0.00000000
## Protestant.Mande 0.00000000
## None.Mole Dagbani 0.16711416
## Catholic.Mole Dagbani 0.11748998
## Jehovah Witness.Mole Dagbani 0.29371106
## Moslem.Mole Dagbani 0.33745803
## Protestant.Mole Dagbani 0.19322559svyby(~sexprt, ~ethnicity, des, svymean, na.rm=T)## ethnicity sexprt se
## Non-Ghanaian Non-Ghanaian 2.936323 0.56387333
## Akan Akan 2.367831 0.06631389
## Ewe Ewe 2.668512 0.17242341
## Ga/Damgme Ga/Damgme 2.632037 0.25049716
## Gruma Gruma 1.642085 0.22985504
## Grusi Grusi 2.072234 0.33956147
## Guan Guan 2.397150 0.23401679
## Mande Mande 1.053315 0.06665944
## Mole Dagbani Mole Dagbani 1.690453 0.09994278#Poisson glm fit to survey data
fit1<-svyglm(sexprt~factor(religion)+factor(ethnicity)+factor(educ)+factor(mrg)+factor(lit)+factor(agec), design=des, family=poisson)
summary(fit1)##
## Call:
## svyglm(formula = sexprt ~ factor(religion) + factor(ethnicity) +
## factor(educ) + factor(mrg) + factor(lit) + factor(agec),
## design = des, family = poisson)
##
## Survey design:
## svydesign(ids = ~HH1, weights = ~wmweight, data = sub)
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.14904 0.22649 0.658 0.510824
## factor(religion)Catholic -0.09021 0.10530 -0.857 0.392048
## factor(religion)Jehovah Witness -0.17196 0.14473 -1.188 0.235346
## factor(religion)Moslem -0.18554 0.12137 -1.529 0.126963
## factor(religion)Protestant -0.04172 0.10153 -0.411 0.681342
## factor(ethnicity)Akan -0.30477 0.16276 -1.873 0.061732 .
## factor(ethnicity)Ewe -0.20530 0.17310 -1.186 0.236208
## factor(ethnicity)Ga/Damgme -0.19880 0.19135 -1.039 0.299353
## factor(ethnicity)Gruma -0.57834 0.24442 -2.366 0.018362 *
## factor(ethnicity)Grusi -0.34555 0.21450 -1.611 0.107835
## factor(ethnicity)Guan -0.25082 0.18704 -1.341 0.180539
## factor(ethnicity)Mande -0.95641 0.19796 -4.831 1.82e-06 ***
## factor(ethnicity)Mole Dagbani -0.54237 0.17067 -3.178 0.001578 **
## factor(educ)Sec 0.03066 0.05879 0.521 0.602277
## factor(mrg)Cohabiting 0.23440 0.06136 3.820 0.000151 ***
## factor(mrg)Single 0.15854 0.05796 2.735 0.006459 **
## factor(lit)Unread 0.07641 0.05639 1.355 0.176018
## factor(agec)(15,25] 0.71598 0.07618 9.399 < 2e-16 ***
## factor(agec)(25,35] 0.91098 0.08529 10.681 < 2e-16 ***
## factor(agec)(35,49] 0.99784 0.07915 12.606 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 0.7973674)
##
## Number of Fisher Scoring iterations: 5#"risk ratios"
round(exp(summary(fit1)$coef[-1,1]), 3)## factor(religion)Catholic factor(religion)Jehovah Witness
## 0.914 0.842
## factor(religion)Moslem factor(religion)Protestant
## 0.831 0.959
## factor(ethnicity)Akan factor(ethnicity)Ewe
## 0.737 0.814
## factor(ethnicity)Ga/Damgme factor(ethnicity)Gruma
## 0.820 0.561
## factor(ethnicity)Grusi factor(ethnicity)Guan
## 0.708 0.778
## factor(ethnicity)Mande factor(ethnicity)Mole Dagbani
## 0.384 0.581
## factor(educ)Sec factor(mrg)Cohabiting
## 1.031 1.264
## factor(mrg)Single factor(lit)Unread
## 1.172 1.079
## factor(agec)(15,25] factor(agec)(25,35]
## 2.046 2.487
## factor(agec)(35,49]
## 2.712We see a significant relationship with the number of sexual partners and the Mande, Gruma and Mole Dagabi tribes. Of these tribes, the Mole Dagbani have higher means of sexual partners in their lifetime. Number of sexual partners happens to increase with age. The lowest mean of sexual partners is attributed to Moslems, compared to other religious groups.
#Overdispersion
fit2<-glm(sexprt~factor(religion)+factor(ethnicity)+factor(educ)+factor(mrg)+factor(lit)+factor(agec), data=wm, family=poisson)
summary(fit2)##
## Call:
## glm(formula = sexprt ~ factor(religion) + factor(ethnicity) +
## factor(educ) + factor(mrg) + factor(lit) + factor(agec),
## family = poisson, data = wm)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.5688 -0.6258 -0.2102 0.3848 6.9500
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.418287 0.573687 0.729 0.465927
## factor(religion)Catholic 0.005449 0.070793 0.077 0.938641
## factor(religion)Jehovah Witness -0.019995 0.119777 -0.167 0.867420
## factor(religion)Moslem -0.075938 0.097512 -0.779 0.436124
## factor(religion)Protestant 0.018617 0.068502 0.272 0.785802
## factor(ethnicity)Akan -0.263069 0.157046 -1.675 0.093913 .
## factor(ethnicity)Ewe -0.237013 0.161482 -1.468 0.142175
## factor(ethnicity)Ga/Damgme -0.122265 0.175290 -0.698 0.485489
## factor(ethnicity)Gruma -0.509611 0.198656 -2.565 0.010309 *
## factor(ethnicity)Grusi -0.492411 0.185115 -2.660 0.007814 **
## factor(ethnicity)Guan -0.271468 0.187043 -1.451 0.146677
## factor(ethnicity)Mande -0.412620 0.368357 -1.120 0.262644
## factor(ethnicity)Mole Dagbani -0.546050 0.159252 -3.429 0.000606 ***
## factor(educ)Prim -0.110431 0.502921 -0.220 0.826199
## factor(educ)Sec -0.079227 0.503248 -0.157 0.874904
## factor(mrg)Cohabiting 0.219884 0.044554 4.935 8.01e-07 ***
## factor(mrg)Single 0.179389 0.045592 3.935 8.33e-05 ***
## factor(lit)Unread 0.096204 0.043698 2.202 0.027697 *
## factor(agec)(15,25] 0.389998 0.222485 1.753 0.079616 .
## factor(agec)(25,35] 0.647386 0.223589 2.895 0.003786 **
## factor(agec)(35,49] 0.707759 0.222904 3.175 0.001497 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1106.29 on 1515 degrees of freedom
## Residual deviance: 941.07 on 1495 degrees of freedom
## (9447 observations deleted due to missingness)
## AIC: 4866.2
##
## Number of Fisher Scoring iterations: 4scale<-sqrt(fit2$deviance/fit2$df.residual)
scale## [1] 0.79339851-pchisq(fit2$deviance, df = fit2$df.residual)## [1] 1P-Value is 1, this model looks to fit the data.
Negative Binomial
library(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(sandwich)
coeftest(fit2, vcov=vcovHC(fit2, type="HC1",cluster="HH1"))##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.4182873 0.2758450 1.5164 0.1294219
## factor(religion)Catholic 0.0054495 0.0588161 0.0927 0.9261791
## factor(religion)Jehovah Witness -0.0199951 0.0999462 -0.2001 0.8414349
## factor(religion)Moslem -0.0759382 0.0773511 -0.9817 0.3262307
## factor(religion)Protestant 0.0186166 0.0574474 0.3241 0.7458895
## factor(ethnicity)Akan -0.2630692 0.1472132 -1.7870 0.0739384
## factor(ethnicity)Ewe -0.2370132 0.1500117 -1.5800 0.1141150
## factor(ethnicity)Ga/Damgme -0.1222651 0.1637645 -0.7466 0.4553106
## factor(ethnicity)Gruma -0.5096106 0.1707263 -2.9850 0.0028362
## factor(ethnicity)Grusi -0.4924106 0.1688965 -2.9155 0.0035517
## factor(ethnicity)Guan -0.2714682 0.1654902 -1.6404 0.1009245
## factor(ethnicity)Mande -0.4126199 0.3267323 -1.2629 0.2066364
## factor(ethnicity)Mole Dagbani -0.5460502 0.1479068 -3.6919 0.0002226
## factor(educ)Prim -0.1104309 0.2078608 -0.5313 0.5952295
## factor(educ)Sec -0.0792274 0.2090168 -0.3790 0.7046522
## factor(mrg)Cohabiting 0.2198836 0.0387191 5.6789 1.355e-08
## factor(mrg)Single 0.1793888 0.0422363 4.2473 2.164e-05
## factor(lit)Unread 0.0962036 0.0426318 2.2566 0.0240322
## factor(agec)(15,25] 0.3899982 0.0968466 4.0270 5.650e-05
## factor(agec)(25,35] 0.6473859 0.0970571 6.6702 2.555e-11
## factor(agec)(35,49] 0.7077594 0.0970678 7.2914 3.068e-13
##
## (Intercept)
## factor(religion)Catholic
## factor(religion)Jehovah Witness
## factor(religion)Moslem
## factor(religion)Protestant
## factor(ethnicity)Akan .
## factor(ethnicity)Ewe
## factor(ethnicity)Ga/Damgme
## factor(ethnicity)Gruma **
## factor(ethnicity)Grusi **
## factor(ethnicity)Guan
## factor(ethnicity)Mande
## factor(ethnicity)Mole Dagbani ***
## factor(educ)Prim
## factor(educ)Sec
## factor(mrg)Cohabiting ***
## factor(mrg)Single ***
## factor(lit)Unread *
## factor(agec)(15,25] ***
## factor(agec)(25,35] ***
## factor(agec)(35,49] ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1library(MASS)##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## selectfit.nb2<-glm.nb(sexprt~factor(religion)+factor(ethnicity)+factor(educ)+factor(mrg)+factor(lit)+factor(agec), data=wm, weights=wmweight/mean(wmweight, na.rm=T))## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached#clx2(fit.nb2,cluster =sub$ststr)
coeftest(fit.nb2, vcov=vcovHC(fit.nb2, type="HC1",cluster="HH1"))##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.3979679 0.2814153 1.4142 0.157313
## factor(religion)Catholic -0.0680760 0.0813079 -0.8373 0.402445
## factor(religion)Jehovah Witness -0.1496399 0.1279830 -1.1692 0.242316
## factor(religion)Moslem -0.1117204 0.0964744 -1.1580 0.246851
## factor(religion)Protestant -0.0096695 0.0793455 -0.1219 0.903005
## factor(ethnicity)Akan -0.2910908 0.1785752 -1.6301 0.103086
## factor(ethnicity)Ewe -0.2534158 0.1815303 -1.3960 0.162715
## factor(ethnicity)Ga/Damgme -0.2208073 0.1968056 -1.1220 0.261881
## factor(ethnicity)Gruma -0.5560135 0.2072359 -2.6830 0.007297
## factor(ethnicity)Grusi -0.3563074 0.2336189 -1.5252 0.127218
## factor(ethnicity)Guan -0.2085018 0.1957672 -1.0651 0.286853
## factor(ethnicity)Mande -0.4852058 0.4288682 -1.1314 0.257902
## factor(ethnicity)Mole Dagbani -0.5497052 0.1828280 -3.0067 0.002641
## factor(educ)Prim -0.0016274 0.1807024 -0.0090 0.992814
## factor(educ)Sec -0.0211594 0.1820377 -0.1162 0.907465
## factor(mrg)Cohabiting 0.2435075 0.0512339 4.7529 2.006e-06
## factor(mrg)Single 0.1635816 0.0505132 3.2384 0.001202
## factor(lit)Unread 0.0519023 0.0473047 1.0972 0.272559
## factor(agec)(15,25] 0.4342010 0.1039770 4.1759 2.968e-05
## factor(agec)(25,35] 0.6869150 0.1074228 6.3945 1.611e-10
## factor(agec)(35,49] 0.7605653 0.1040890 7.3069 2.734e-13
##
## (Intercept)
## factor(religion)Catholic
## factor(religion)Jehovah Witness
## factor(religion)Moslem
## factor(religion)Protestant
## factor(ethnicity)Akan
## factor(ethnicity)Ewe
## factor(ethnicity)Ga/Damgme
## factor(ethnicity)Gruma **
## factor(ethnicity)Grusi
## factor(ethnicity)Guan
## factor(ethnicity)Mande
## factor(ethnicity)Mole Dagbani **
## factor(educ)Prim
## factor(educ)Sec
## factor(mrg)Cohabiting ***
## factor(mrg)Single **
## factor(lit)Unread
## factor(agec)(15,25] ***
## factor(agec)(25,35] ***
## factor(agec)(35,49] ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(fit.nb2)##
## Call:
## glm.nb(formula = sexprt ~ factor(religion) + factor(ethnicity) +
## factor(educ) + factor(mrg) + factor(lit) + factor(agec),
## data = wm, weights = wmweight/mean(wmweight, na.rm = T),
## init.theta = 40557.95952, link = log)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.0505 -0.5628 -0.1736 0.3216 6.8058
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.397968 0.666190 0.597 0.550254
## factor(religion)Catholic -0.068076 0.061064 -1.115 0.264923
## factor(religion)Jehovah Witness -0.149640 0.102695 -1.457 0.145080
## factor(religion)Moslem -0.111720 0.076075 -1.469 0.141953
## factor(religion)Protestant -0.009669 0.056930 -0.170 0.865129
## factor(ethnicity)Akan -0.291091 0.131613 -2.212 0.026986 *
## factor(ethnicity)Ewe -0.253416 0.134470 -1.885 0.059490 .
## factor(ethnicity)Ga/Damgme -0.220807 0.142718 -1.547 0.121826
## factor(ethnicity)Gruma -0.556014 0.197869 -2.810 0.004954 **
## factor(ethnicity)Grusi -0.356307 0.162428 -2.194 0.028261 *
## factor(ethnicity)Guan -0.208502 0.154847 -1.347 0.178140
## factor(ethnicity)Mande -0.485206 0.361431 -1.342 0.179448
## factor(ethnicity)Mole Dagbani -0.549705 0.142855 -3.848 0.000119 ***
## factor(educ)Prim -0.001627 0.604552 -0.003 0.997852
## factor(educ)Sec -0.021159 0.604695 -0.035 0.972086
## factor(mrg)Cohabiting 0.243507 0.036419 6.686 2.29e-11 ***
## factor(mrg)Single 0.163582 0.040712 4.018 5.87e-05 ***
## factor(lit)Unread 0.051902 0.036561 1.420 0.155718
## factor(agec)(15,25] 0.434201 0.243571 1.783 0.074644 .
## factor(agec)(25,35] 0.686915 0.244117 2.814 0.004895 **
## factor(agec)(35,49] 0.760565 0.243566 3.123 0.001792 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Negative Binomial(40557.96) family taken to be 1)
##
## Null deviance: 1429.7 on 1515 degrees of freedom
## Residual deviance: 1253.7 on 1495 degrees of freedom
## (9447 observations deleted due to missingness)
## AIC: 6377.7
##
## Number of Fisher Scoring iterations: 1
##
##
## Theta: 40558
## Std. Err.: 143099
## Warning while fitting theta: iteration limit reached
##
## 2 x log-likelihood: -6333.73AIC for the Poisson Model (Computed in our dispersion test) computes to 4866.2, whereas our Negative Binomial Model computes to 6377.7. Thus, we can conclude that the Poisson Model works best for this particular analysis. It is neccesary to note however, that the Negative Binomial model has more signficant predictors than the former model.