The Vaccinators tried to build a model to understand whether highly variant childhood immunisation rates across Australia would improve using multiple predictors, including: - Geographic variables: electorate, Primary Health Network Area, SA3, postcode level - Main variable of interest: percentage immunisation rate of a given geographic area (classed as pc_immun and pc_immun_class in our datasets) - Non-geographic variables we hypothesised might influence the childhood vaccination rate included: demographics, political party in power in a particular Federal electorate,mean taxable income and the four different SEIFA indexes
With the multitude of different variables - some continuous, others categorical - it’s highly likely our dataset has what is called “confounding” variables. Confounding variables - which are apparently different to nuisance variables, which increase variability - are named as such because they
#import merged data which includes immunisation coverage, postcode, PHN, Electorate, SEIFA deciles and ranks and mean taxable income per postcode
everything <- read.csv("../cleaned_data/immunization_with_everything_taxation_update.csv")
str(everything)## 'data.frame': 191163 obs. of 51 variables:
## $ X.2 : int 1 2 3 4 5 6 7 8 9 10 ...
## $ X.1 : int 1 7 9 10 14 17 25 45 48 49 ...
## $ postcode : int 800 800 800 800 800 800 800 800 800 800 ...
## $ X : int 163657 163658 163662 163663 163661 163665 163656 163660 163659 163654 ...
## $ state.x : Factor w/ 12 levels "ACT","NSW","NSW/ACT",..: 6 6 6 6 6 6 6 6 6 6 ...
## $ year : int 2016 2016 2016 2016 2016 2016 2016 2016 2016 2016 ...
## $ age : int 5 2 1 1 2 1 5 2 2 5 ...
## $ pc_immun : Factor w/ 9 levels "<70.0","70.0-74.9",..: 6 3 6 6 3 6 6 3 3 6 ...
## $ caution : int 1 1 1 1 1 1 1 1 1 1 ...
## $ pc_immun_class : int 6 3 6 6 3 6 6 3 3 6 ...
## $ PHN_code : Factor w/ 31 levels "PHN101","PHN102",..: 30 30 30 30 30 30 30 30 30 30 ...
## $ PHN_number : int 701 701 701 701 701 701 701 701 701 701 ...
## $ Index.type : Factor w/ 4 levels "Index of Economic Resources",..: 4 3 3 2 4 4 1 1 2 3 ...
## $ Time : int 2016 2016 2016 2016 2016 2016 2016 2016 2016 2016 ...
## $ Maximum.score.for.SA1s.in.area : int NA 1167 1167 1163 NA NA 1019 1019 1163 1167 ...
## $ Minimum.score.for.SA1s.in.area : int 842 914 914 1023 842 842 751 751 1023 914 ...
## $ Rank.within.Australia : int 2243 2398 2398 2287 2243 2243 412 412 2287 2398 ...
## $ Rank.within.Australia...Decile : int NA 10 10 9 NA NA 2 2 9 10 ...
## $ Rank.within.Australia...Percentile : int 86 92 92 87 86 86 16 16 87 92 ...
## $ Rank.within.State.or.Territory : int 28 33 33 33 28 28 18 18 33 33 ...
## $ Rank.within.State.or.Territory...Decile : int 8 10 10 10 8 8 6 6 10 10 ...
## $ Rank.within.State.or.Territory...Percentile: int NA 92 92 92 NA NA 51 51 92 92 ...
## $ Score : int 1066 1096 1096 1089 1066 1066 946 946 1089 1096 ...
## $ Usual.resident.population : int 6464 6464 6464 6464 6464 6464 6464 6464 6464 6464 ...
## $ Electoral.division : Factor w/ 150 levels "Adelaide","Aston",..: 136 136 136 136 136 136 136 136 136 136 ...
## $ Per.cent.postcode.in.electorate : num 100 100 100 100 100 100 100 100 100 100 ...
## $ DivisionID2016 : int 307 307 307 307 307 307 307 307 307 307 ...
## $ StateAB2016 : Factor w/ 8 levels "ACT","NSW","NT",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ CandidateID2016 : int 28737 28737 28737 28737 28737 28737 28737 28737 28737 28737 ...
## $ GivenNm2016 : Factor w/ 97 levels "Adam","Alan",..: 56 56 56 56 56 56 56 56 56 56 ...
## $ Surname2016 : Factor w/ 135 levels "ABBOTT","ALBANESE",..: 51 51 51 51 51 51 51 51 51 51 ...
## $ PartyNm2016 : Factor w/ 8 levels "Australian Labor Party",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ PartyAb2016 : Factor w/ 8 levels "ALP","GRN","IND",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ DivisionID2010 : int 307 307 307 307 307 307 307 307 307 307 ...
## $ StateAb2010 : Factor w/ 8 levels "ACT","NSW","NT",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ CandidateID2010 : int 21477 21477 21477 21477 21477 21477 21477 21477 21477 21477 ...
## $ GivenNm2010 : Factor w/ 108 levels "Adam","Alan",..: 74 74 74 74 74 74 74 74 74 74 ...
## $ Surname2010 : Factor w/ 137 levels "ABBOTT","ADAMS",..: 52 52 52 52 52 52 52 52 52 52 ...
## $ PartyNm2010 : Factor w/ 7 levels "Australian Labor Party",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ PartyAb2010 : Factor w/ 7 levels "ALP","CLP","GRN",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ DivisionID2013 : int 307 307 307 307 307 307 307 307 307 307 ...
## $ StateAb2013 : Factor w/ 8 levels "ACT","NSW","NT",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ CandidateID2013 : int 23502 23502 23502 23502 23502 23502 23502 23502 23502 23502 ...
## $ GivenNm2013 : Factor w/ 106 levels "Adam","Alan",..: 76 76 76 76 76 76 76 76 76 76 ...
## $ Surname2013 : Factor w/ 140 levels "ABBOTT","ALBANESE",..: 48 48 48 48 48 48 48 48 48 48 ...
## $ PartyNm2013 : Factor w/ 9 levels "Australian Labor Party",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ PartyAb2013 : Factor w/ 9 levels "ALP","CLP","GRN",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ state.y : Factor w/ 8 levels "ACT","NSW","NT",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ num_individuals : int 5464 5464 5464 5464 5464 5464 5464 5464 5464 5464 ...
## $ total_tax : num 389375576 389375576 389375576 389375576 389375576 ...
## $ mean_tax : int 71263 71263 71263 71263 71263 71263 71263 71263 71263 71263 ...#cleaning the data, filter out 0 which is NP in immunisation coverage
everything_new <- everything %>%
filter(pc_immun_class != 0)Try a simple lm with pc immun class to explore adjustment. This model is testing whether the class of percentage immunisation can be explained by mean tax or SEIFA score
modela <- lm(pc_immun_class ~ mean_tax + Score, data = everything)
summary(modela)##
## Call:
## lm(formula = pc_immun_class ~ mean_tax + Score, data = everything)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.029 -3.777 1.013 2.502 4.731
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.3179962868 0.0987466427 13.35 <0.0000000000000002 ***
## mean_tax 0.0000383746 0.0000005472 70.13 <0.0000000000000002 ***
## Score 0.0011089027 0.0001114466 9.95 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.023 on 185640 degrees of freedom
## (5520 observations deleted due to missingness)
## Multiple R-squared: 0.042, Adjusted R-squared: 0.04199
## F-statistic: 4069 on 2 and 185640 DF, p-value: < 0.00000000000000022It reveals that our pc_immun_class variable can only be explained by 0.09% of the independent variables of mean tax and SEIFA score. It also reveals a low p-value < 0.00000000000000022.
#Try another simple lm with pc_immun_class and postcode and PHN and state
modelb <- lm(pc_immun_class ~ postcode + PHN_number + state.x, data = everything)
summary(modelb)##
## Call:
## lm(formula = pc_immun_class ~ postcode + PHN_number + state.x,
## data = everything)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.4699 -2.9380 0.7142 2.2163 6.8972
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.80127396 0.30562082 45.158 < 0.0000000000000002 ***
## postcode -0.00326249 0.00002559 -127.473 < 0.0000000000000002 ***
## PHN_number 0.00118882 0.00037945 3.133 0.001730 **
## state.xNSW -0.90035085 0.26518165 -3.395 0.000686 ***
## state.xNSW/ACT -0.10446229 0.26785830 -0.390 0.696544
## state.xNSW/QLD -2.43669870 0.29758170 -8.188 0.000000000000000266 ***
## state.xNSW/VIC 4.51018234 0.35255728 12.793 < 0.0000000000000002 ***
## state.xNT -8.17548922 0.10941930 -74.717 < 0.0000000000000002 ***
## state.xQLD 5.13355679 0.20328923 25.252 < 0.0000000000000002 ***
## state.xSA 6.46394485 0.17873032 36.166 < 0.0000000000000002 ***
## state.xSA/WA/NT -5.65641438 0.27827855 -20.326 < 0.0000000000000002 ***
## state.xTAS 12.61103731 0.15813532 79.748 < 0.0000000000000002 ***
## state.xVIC 1.25487017 0.23274372 5.392 0.000000069900271009 ***
## state.xWA 9.45972485 0.16293115 58.060 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.899 on 191149 degrees of freedom
## Multiple R-squared: 0.1262, Adjusted R-squared: 0.1261
## F-statistic: 2123 on 13 and 191149 DF, p-value: < 0.00000000000000022Adding more variables is showing that the small combined states (which come from the postcode merge) are three-asterisk predictors of pc_immun_class, which is a bit of nonsense really because those states like NSW/ACT and SA/WA/NT are actually quirks of the postcode system rather than actual states. It makes sense that the state of NSW on its own is a reasonable predictor (compared to other states) because it has the largest volume of entries.
#Let's try a really obvious adjustment scenario to put pc_immun_class pc_immun against each other
modelc <- lm(pc_immun_class ~ pc_immun + postcode, data = everything)
summary(modelc)##
## Call:
## lm(formula = pc_immun_class ~ pc_immun + postcode, data = everything)
##
## Residuals:
## Min 1Q Median 3Q
## -0.0000000035481 0.0000000000000 0.0000000000000 0.0000000000001
## Max
## 0.0000000007636
##
## Coefficients:
## Estimate Std. Error
## (Intercept) 1.00000000000037903014 0.00000000000053659524
## pc_immun70.0-74.9 1.00000000000321520588 0.00000000000066294716
## pc_immun75.0-79.9 1.99999999999336619538 0.00000000000058647569
## pc_immun80.0-84.9 2.99999999999695932118 0.00000000000054855617
## pc_immun85.0-89.9 4.00000000000674305056 0.00000000000053703560
## pc_immun90.0-92.4 4.99999999998323829686 0.00000000000053643010
## pc_immun92.5-94.9 6.00000000000528377342 0.00000000000053627332
## pc_immun95.0-100.0 7.00000000001493472013 0.00000000000053704891
## pc_immunNP -0.99999999999940381024 0.00000000000053547613
## postcode 0.00000000000000004074 0.00000000000000001544
## t value Pr(>|t|)
## (Intercept) 1863602073876.605 < 0.0000000000000002 ***
## pc_immun70.0-74.9 1508415841004.140 < 0.0000000000000002 ***
## pc_immun75.0-79.9 3410201033037.085 < 0.0000000000000002 ***
## pc_immun80.0-84.9 5468902119890.580 < 0.0000000000000002 ***
## pc_immun85.0-89.9 7448295737938.922 < 0.0000000000000002 ***
## pc_immun90.0-92.4 9320878956143.711 < 0.0000000000000002 ***
## pc_immun92.5-94.9 11188324556689.053 < 0.0000000000000002 ***
## pc_immun95.0-100.0 13034194592752.377 < 0.0000000000000002 ***
## pc_immunNP -1867496885626.615 < 0.0000000000000002 ***
## postcode 2.639 0.00832 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.000000000009726 on 191153 degrees of freedom
## Multiple R-squared: 1, Adjusted R-squared: 1
## F-statistic: 2.16e+27 on 9 and 191153 DF, p-value: < 0.00000000000000022Which is just common sense, as pc_immun is the percentage range and pc_immun_class was a dummy variable that assigns a number to each pc_immun rank.
#Try a more complex lm with a lot more variables to see the impact on the model
model1 <- lm(pc_immun_class ~ mean_tax + state.x + PartyNm2016 + Score + Electoral.division, data = everything)
summary(model1)##
## Call:
## lm(formula = pc_immun_class ~ mean_tax + state.x + PartyNm2016 +
## Score + Electoral.division, data = everything)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.1506 -1.8558 0.0311 1.6672 7.2258
##
## Coefficients: (9 not defined because of singularities)
## Estimate Std. Error t value
## (Intercept) 5.6917226909 0.3525420232 16.145
## mean_tax 0.0000180647 0.0000006865 26.314
## state.xNSW 0.2812538265 0.2540760901 1.107
## state.xNSW/ACT 0.8436600719 0.2245970404 3.756
## state.xNSW/QLD 4.6772802505 0.6384505162 7.326
## state.xNSW/VIC 4.5028378119 0.3660384887 12.302
## state.xNT 3.1787248361 0.5275658611 6.025
## state.xQLD 6.5633851749 0.6065791550 10.820
## state.xSA 0.4876349306 0.3410688961 1.430
## state.xSA/WA/NT 5.6961159870 0.4623400439 12.320
## state.xTAS -2.1646839884 0.3373798972 -6.416
## state.xVIC 1.1382250271 0.3178130276 3.581
## state.xWA 0.2693360557 0.5780348331 0.466
## PartyNm2016Independent -4.1888529002 0.1132758236 -36.979
## PartyNm2016Katter's Australian Party -7.2199129305 0.5095914171 -14.168
## PartyNm2016Liberal -1.3351031772 0.2393828533 -5.577
## PartyNm2016Liberal National Party -5.5970617339 0.5158102947 -10.851
## PartyNm2016Nick Xenophon Team -3.0727755725 0.0834174889 -36.836
## PartyNm2016The Greens -0.8305821320 0.1259082915 -6.597
## PartyNm2016The Nationals -0.9831155360 0.2262764972 -4.345
## Score -0.0015168591 0.0001156403 -13.117
## Electoral.divisionAston 1.7948310515 0.2398014056 7.485
## Electoral.divisionBallarat -1.6706037683 0.1280161628 -13.050
## Electoral.divisionBanks 2.4709620265 0.1444773607 17.103
## Electoral.divisionBarker -1.5851452004 0.2554225910 -6.206
## Electoral.divisionBarton 0.5117290059 0.2370780503 2.158
## Electoral.divisionBass -0.5001804016 0.0879947283 -5.684
## Electoral.divisionBatman 0.1287820763 0.1619262024 0.795
## Electoral.divisionBendigo -3.3959820802 0.1221969905 -27.791
## Electoral.divisionBennelong 1.9366798431 0.1534400444 12.622
## Electoral.divisionBerowra 1.4206346027 0.1264062657 11.239
## Electoral.divisionBlair -6.7986608823 0.5110546116 -13.303
## Electoral.divisionBlaxland 0.5067087266 0.2328723511 2.176
## Electoral.divisionBonner -0.0437428735 0.1236172657 -0.354
## Electoral.divisionBoothby 1.5344022671 0.2611797046 5.875
## Electoral.divisionBowman -0.1006505993 0.1345692412 -0.748
## Electoral.divisionBraddon 2.6795315785 0.1044578016 25.652
## Electoral.divisionBradfield 1.0176977427 0.1323379648 7.690
## Electoral.divisionBrand -0.5137884261 0.4804114742 -1.069
## Electoral.divisionBrisbane 0.2481368355 0.1318057041 1.883
## Electoral.divisionBruce -0.5579610216 0.1623759219 -3.436
## Electoral.divisionCalare -0.7772177932 0.0933926998 -8.322
## Electoral.divisionCalwell -0.8757119137 0.1393000130 -6.287
## Electoral.divisionCanberra 0.5522207893 0.3268974121 1.689
## Electoral.divisionCanning -0.1655441466 0.5354088433 -0.309
## Electoral.divisionCapricornia -1.6186975489 0.1175318120 -13.772
## Electoral.divisionCasey 0.0522376636 0.2278071551 0.229
## Electoral.divisionChifley 0.7115140938 0.2461385942 2.891
## Electoral.divisionChisholm 1.2114860910 0.2336162285 5.186
## Electoral.divisionCook 2.5935338785 0.1525126193 17.005
## Electoral.divisionCorangamite -1.7759069754 0.2240805723 -7.925
## Electoral.divisionCorio -0.2710626330 0.1383854967 -1.959
## Electoral.divisionCowan 0.1960047411 0.4832265258 0.406
## Electoral.divisionCowper 0.6907794586 0.1012114426 6.825
## Electoral.divisionCunningham 1.2484973333 0.2397108414 5.208
## Electoral.divisionCurtin 0.6647875445 0.5343191847 1.244
## Electoral.divisionDawson -1.7959339712 0.1199992222 -14.966
## Electoral.divisionDeakin 1.7423159419 0.2395255126 7.274
## Electoral.divisionDenison 7.2298322311 0.1498600965 48.244
## Electoral.divisionDickson 0.7868943156 0.1344342589 5.853
## Electoral.divisionDobell 1.5039749063 0.2457143933 6.121
## Electoral.divisionDunkley 1.5090525386 0.2424572481 6.224
## Electoral.divisionEden-Monaro -1.2569800319 0.2274394390 -5.527
## Electoral.divisionFadden 0.2221480056 0.1418928117 1.566
## Electoral.divisionFairfax -1.7478782636 0.1256191710 -13.914
## Electoral.divisionFarrer -0.4183744235 0.1167898102 -3.582
## Electoral.divisionFisher -1.2754011711 0.1305563329 -9.769
## Electoral.divisionFlinders -0.6645349874 0.2232057712 -2.977
## Electoral.divisionForde -0.3450900155 0.1184978605 -2.912
## Electoral.divisionForrest -1.3845769068 0.5332607858 -2.596
## Electoral.divisionFowler 0.5179051814 0.2457326508 2.108
## Electoral.divisionFranklin 1.3769314347 0.0781767249 17.613
## Electoral.divisionFremantle -0.7432114936 0.4822166908 -1.541
## Electoral.divisionGellibrand 0.1809136666 0.1409171969 1.284
## Electoral.divisionGilmore 1.4732801207 0.1436695765 10.255
## Electoral.divisionGippsland -2.4360390420 0.2082001365 -11.700
## Electoral.divisionGoldstein 1.2241300849 0.2333968632 5.245
## Electoral.divisionGorton 0.0410341998 0.1499067627 0.274
## Electoral.divisionGrayndler 1.0097521932 0.2327727013 4.338
## Electoral.divisionGreenway 1.4806686328 0.2392739595 6.188
## Electoral.divisionGrey -2.9335243566 0.2537467981 -11.561
## Electoral.divisionGriffith -5.6343546572 0.5143270547 -10.955
## Electoral.divisionGroom -2.1834211558 0.1258420400 -17.350
## Electoral.divisionHasluck 1.4962946603 0.5397401828 2.772
## Electoral.divisionHerbert -5.6553662743 0.5168416553 -10.942
## Electoral.divisionHiggins 1.0422051094 0.2298801690 4.534
## Electoral.divisionHindmarsh -0.0321107973 0.1000217354 -0.321
## Electoral.divisionHinkler -2.5740570037 0.1270833079 -20.255
## Electoral.divisionHolt 0.1423827674 0.1410425702 1.010
## Electoral.divisionHotham -0.0157740080 0.1311736130 -0.120
## Electoral.divisionHughes 3.0408845041 0.1478026135 20.574
## Electoral.divisionHume 1.2429695370 0.1178218016 10.550
## Electoral.divisionHunter 1.5069475632 0.2330001417 6.468
## Electoral.divisionIndi NA NA NA
## Electoral.divisionIsaacs 0.2352965141 0.1377664236 1.708
## Electoral.divisionJagajaga 0.1765776471 0.1355419288 1.303
## Electoral.divisionKennedy NA NA NA
## Electoral.divisionKingsford Smith 0.2355274967 0.2395988013 0.983
## Electoral.divisionKingston -0.1693168968 0.1048212327 -1.615
## Electoral.divisionKooyong 1.1494797858 0.2315123391 4.965
## Electoral.divisionLa Trobe 0.2836736495 0.2266595029 1.252
## Electoral.divisionLalor -0.5182130599 0.1426277622 -3.633
## Electoral.divisionLeichhardt 0.4752775157 0.1354411965 3.509
## Electoral.divisionLilley -5.6323244469 0.5131990471 -10.975
## Electoral.divisionLindsay 0.9166446803 0.2373865564 3.861
## Electoral.divisionLingiari -5.5385752876 0.4055154285 -13.658
## Electoral.divisionLongman -5.5063159700 0.5122305890 -10.750
## Electoral.divisionLyne 0.1160472154 0.1093388243 1.061
## Electoral.divisionLyons NA NA NA
## Electoral.divisionMacarthur 0.7734526147 0.2398467911 3.225
## Electoral.divisionMackellar 0.6901729413 0.1276999993 5.405
## Electoral.divisionMacquarie -0.6711510512 0.2288221478 -2.933
## Electoral.divisionMakin 0.7091711566 0.1068310733 6.638
## Electoral.divisionMallee -3.5410853915 0.2060820974 -17.183
## Electoral.divisionMaranoa -3.7151005681 0.1060581191 -35.029
## Electoral.divisionMaribyrnong 0.1514291203 0.1446339793 1.047
## Electoral.divisionMayo NA NA NA
## Electoral.divisionMcEwen -2.2635521279 0.1116148143 -20.280
## Electoral.divisionMcMillan -1.5538755474 0.2244713906 -6.922
## Electoral.divisionMcPherson -1.2169711432 0.1363257555 -8.927
## Electoral.divisionMelbourne NA NA NA
## Electoral.divisionMelbourne Ports -0.9056517066 0.1304284125 -6.944
## Electoral.divisionMenzies 0.8882211354 0.2332946256 3.807
## Electoral.divisionMitchell 2.3332638167 0.1392126580 16.760
## Electoral.divisionMoncrieff -0.2116968024 0.1466074994 -1.444
## Electoral.divisionMoore 1.6858694510 0.5469012033 3.083
## Electoral.divisionMoreton -5.8602740957 0.5125919740 -11.433
## Electoral.divisionMurray -3.0447111274 0.2051209349 -14.843
## Electoral.divisionNew England -0.9219886591 0.0895470291 -10.296
## Electoral.divisionNewcastle 0.4152819722 0.2281059537 1.821
## Electoral.divisionNorth Sydney 0.8674115879 0.1285821180 6.746
## Electoral.divisionO'Connor -3.0344832381 0.5314531559 -5.710
## Electoral.divisionOxley -5.3152290326 0.5142710242 -10.335
## Electoral.divisionPage 0.1125490763 0.1019792396 1.104
## Electoral.divisionParkes -0.5238090381 0.0876549879 -5.976
## Electoral.divisionParramatta 0.8047089383 0.2355396653 3.416
## Electoral.divisionPaterson -0.0511911514 0.2277392229 -0.225
## Electoral.divisionPearce -1.0320924903 0.5320262405 -1.940
## Electoral.divisionPerth -0.4854040032 0.4790594999 -1.013
## Electoral.divisionPetrie 0.6368840047 0.1278566148 4.981
## Electoral.divisionPort Adelaide 0.0516536811 0.1001057224 0.516
## Electoral.divisionRankin -5.3761400386 0.5133008152 -10.474
## Electoral.divisionReid 1.5034607313 0.1362929081 11.031
## Electoral.divisionRichmond -1.2393309765 0.2317429028 -5.348
## Electoral.divisionRiverina NA NA NA
## Electoral.divisionRobertson 1.0677894468 0.1567365820 6.813
## Electoral.divisionRyan NA NA NA
## Electoral.divisionScullin 0.0510075194 0.1414093997 0.361
## Electoral.divisionShortland 1.7680597706 0.2393250760 7.388
## Electoral.divisionSolomon -3.2263000417 0.4231162122 -7.625
## Electoral.divisionStirling 1.3527209597 0.5384498225 2.512
## Electoral.divisionSturt 1.5403254599 0.2601218094 5.922
## Electoral.divisionSwan 1.0122056912 0.5394401772 1.876
## Electoral.divisionSydney -0.5070591462 0.2282285925 -2.222
## Electoral.divisionTangney 1.2677892366 0.5393390148 2.351
## Electoral.divisionWakefield -1.6687053834 0.0900907004 -18.523
## Electoral.divisionWannon -2.4656897444 0.2221639184 -11.099
## Electoral.divisionWarringah 1.1656422717 0.1357734579 8.585
## Electoral.divisionWatson 0.5971072642 0.2327124155 2.566
## Electoral.divisionWentworth NA NA NA
## Electoral.divisionWerriwa 0.5704882708 0.2398967314 2.378
## Electoral.divisionWills NA NA NA
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## mean_tax < 0.0000000000000002 ***
## state.xNSW 0.268310
## state.xNSW/ACT 0.000172 ***
## state.xNSW/QLD 0.00000000000023816 ***
## state.xNSW/VIC < 0.0000000000000002 ***
## state.xNT 0.00000000169168273 ***
## state.xQLD < 0.0000000000000002 ***
## state.xSA 0.152798
## state.xSA/WA/NT < 0.0000000000000002 ***
## state.xTAS 0.00000000014010952 ***
## state.xVIC 0.000342 ***
## state.xWA 0.641251
## PartyNm2016Independent < 0.0000000000000002 ***
## PartyNm2016Katter's Australian Party < 0.0000000000000002 ***
## PartyNm2016Liberal 0.00000002446812490 ***
## PartyNm2016Liberal National Party < 0.0000000000000002 ***
## PartyNm2016Nick Xenophon Team < 0.0000000000000002 ***
## PartyNm2016The Greens 0.00000000004215404 ***
## PartyNm2016The Nationals 0.00001395110472936 ***
## Score < 0.0000000000000002 ***
## Electoral.divisionAston 0.00000000000007207 ***
## Electoral.divisionBallarat < 0.0000000000000002 ***
## Electoral.divisionBanks < 0.0000000000000002 ***
## Electoral.divisionBarker 0.00000000054481942 ***
## Electoral.divisionBarton 0.030892 *
## Electoral.divisionBass 0.00000001316287137 ***
## Electoral.divisionBatman 0.426432
## Electoral.divisionBendigo < 0.0000000000000002 ***
## Electoral.divisionBennelong < 0.0000000000000002 ***
## Electoral.divisionBerowra < 0.0000000000000002 ***
## Electoral.divisionBlair < 0.0000000000000002 ***
## Electoral.divisionBlaxland 0.029564 *
## Electoral.divisionBonner 0.723446
## Electoral.divisionBoothby 0.00000000423887112 ***
## Electoral.divisionBowman 0.454493
## Electoral.divisionBraddon < 0.0000000000000002 ***
## Electoral.divisionBradfield 0.00000000000001477 ***
## Electoral.divisionBrand 0.284857
## Electoral.divisionBrisbane 0.059757 .
## Electoral.divisionBruce 0.000590 ***
## Electoral.divisionCalare < 0.0000000000000002 ***
## Electoral.divisionCalwell 0.00000000032543201 ***
## Electoral.divisionCanberra 0.091168 .
## Electoral.divisionCanning 0.757176
## Electoral.divisionCapricornia < 0.0000000000000002 ***
## Electoral.divisionCasey 0.818631
## Electoral.divisionChifley 0.003844 **
## Electoral.divisionChisholm 0.00000021533387174 ***
## Electoral.divisionCook < 0.0000000000000002 ***
## Electoral.divisionCorangamite 0.00000000000000229 ***
## Electoral.divisionCorio 0.050144 .
## Electoral.divisionCowan 0.685025
## Electoral.divisionCowper 0.00000000000881421 ***
## Electoral.divisionCunningham 0.00000019074584905 ***
## Electoral.divisionCurtin 0.213436
## Electoral.divisionDawson < 0.0000000000000002 ***
## Electoral.divisionDeakin 0.00000000000035037 ***
## Electoral.divisionDenison < 0.0000000000000002 ***
## Electoral.divisionDickson 0.00000000482551053 ***
## Electoral.divisionDobell 0.00000000093289396 ***
## Electoral.divisionDunkley 0.00000000048575244 ***
## Electoral.divisionEden-Monaro 0.00000003268534110 ***
## Electoral.divisionFadden 0.117443
## Electoral.divisionFairfax < 0.0000000000000002 ***
## Electoral.divisionFarrer 0.000341 ***
## Electoral.divisionFisher < 0.0000000000000002 ***
## Electoral.divisionFlinders 0.002909 **
## Electoral.divisionForde 0.003589 **
## Electoral.divisionForrest 0.009420 **
## Electoral.divisionFowler 0.035067 *
## Electoral.divisionFranklin < 0.0000000000000002 ***
## Electoral.divisionFremantle 0.123260
## Electoral.divisionGellibrand 0.199203
## Electoral.divisionGilmore < 0.0000000000000002 ***
## Electoral.divisionGippsland < 0.0000000000000002 ***
## Electoral.divisionGoldstein 0.00000015659688339 ***
## Electoral.divisionGorton 0.784291
## Electoral.divisionGrayndler 0.00001439102260022 ***
## Electoral.divisionGreenway 0.00000000061000347 ***
## Electoral.divisionGrey < 0.0000000000000002 ***
## Electoral.divisionGriffith < 0.0000000000000002 ***
## Electoral.divisionGroom < 0.0000000000000002 ***
## Electoral.divisionHasluck 0.005568 **
## Electoral.divisionHerbert < 0.0000000000000002 ***
## Electoral.divisionHiggins 0.00000580009572155 ***
## Electoral.divisionHindmarsh 0.748182
## Electoral.divisionHinkler < 0.0000000000000002 ***
## Electoral.divisionHolt 0.312735
## Electoral.divisionHotham 0.904283
## Electoral.divisionHughes < 0.0000000000000002 ***
## Electoral.divisionHume < 0.0000000000000002 ***
## Electoral.divisionHunter 0.00000000009984552 ***
## Electoral.divisionIndi NA
## Electoral.divisionIsaacs 0.087650 .
## Electoral.divisionJagajaga 0.192661
## Electoral.divisionKennedy NA
## Electoral.divisionKingsford Smith 0.325605
## Electoral.divisionKingston 0.106249
## Electoral.divisionKooyong 0.00000068733615328 ***
## Electoral.divisionLa Trobe 0.210739
## Electoral.divisionLalor 0.000280 ***
## Electoral.divisionLeichhardt 0.000450 ***
## Electoral.divisionLilley < 0.0000000000000002 ***
## Electoral.divisionLindsay 0.000113 ***
## Electoral.divisionLingiari < 0.0000000000000002 ***
## Electoral.divisionLongman < 0.0000000000000002 ***
## Electoral.divisionLyne 0.288530
## Electoral.divisionLyons NA
## Electoral.divisionMacarthur 0.001261 **
## Electoral.divisionMackellar 0.00000006502241235 ***
## Electoral.divisionMacquarie 0.003357 **
## Electoral.divisionMakin 0.00000000003183588 ***
## Electoral.divisionMallee < 0.0000000000000002 ***
## Electoral.divisionMaranoa < 0.0000000000000002 ***
## Electoral.divisionMaribyrnong 0.295110
## Electoral.divisionMayo NA
## Electoral.divisionMcEwen < 0.0000000000000002 ***
## Electoral.divisionMcMillan 0.00000000000445654 ***
## Electoral.divisionMcPherson < 0.0000000000000002 ***
## Electoral.divisionMelbourne NA
## Electoral.divisionMelbourne Ports 0.00000000000383374 ***
## Electoral.divisionMenzies 0.000141 ***
## Electoral.divisionMitchell < 0.0000000000000002 ***
## Electoral.divisionMoncrieff 0.148749
## Electoral.divisionMoore 0.002052 **
## Electoral.divisionMoreton < 0.0000000000000002 ***
## Electoral.divisionMurray < 0.0000000000000002 ***
## Electoral.divisionNew England < 0.0000000000000002 ***
## Electoral.divisionNewcastle 0.068675 .
## Electoral.divisionNorth Sydney 0.00000000001524761 ***
## Electoral.divisionO'Connor 0.00000001133020834 ***
## Electoral.divisionOxley < 0.0000000000000002 ***
## Electoral.divisionPage 0.269748
## Electoral.divisionParkes 0.00000000229400439 ***
## Electoral.divisionParramatta 0.000635 ***
## Electoral.divisionPaterson 0.822151
## Electoral.divisionPearce 0.052390 .
## Electoral.divisionPerth 0.310945
## Electoral.divisionPetrie 0.00000063239611596 ***
## Electoral.divisionPort Adelaide 0.605861
## Electoral.divisionRankin < 0.0000000000000002 ***
## Electoral.divisionReid < 0.0000000000000002 ***
## Electoral.divisionRichmond 0.00000008910692429 ***
## Electoral.divisionRiverina NA
## Electoral.divisionRobertson 0.00000000000961349 ***
## Electoral.divisionRyan NA
## Electoral.divisionScullin 0.718318
## Electoral.divisionShortland 0.00000000000015006 ***
## Electoral.divisionSolomon 0.00000000000002451 ***
## Electoral.divisionStirling 0.011997 *
## Electoral.divisionSturt 0.00000000319507437 ***
## Electoral.divisionSwan 0.060602 .
## Electoral.divisionSydney 0.026304 *
## Electoral.divisionTangney 0.018743 *
## Electoral.divisionWakefield < 0.0000000000000002 ***
## Electoral.divisionWannon < 0.0000000000000002 ***
## Electoral.divisionWarringah < 0.0000000000000002 ***
## Electoral.divisionWatson 0.010293 *
## Electoral.divisionWentworth NA
## Electoral.divisionWerriwa 0.017405 *
## Electoral.divisionWills NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.573 on 174248 degrees of freedom
## (16762 observations deleted due to missingness)
## Multiple R-squared: 0.3018, Adjusted R-squared: 0.3012
## F-statistic: 495.5 on 152 and 174248 DF, p-value: < 0.00000000000000022This is because so many variables have lowered the p-value compared to modela and modelb. It’s also found 5 ‘singularities’ in those variables, mostly with electorates.
#explore the singularities
alias(model1) ## Model :
## pc_immun_class ~ mean_tax + state.x + PartyNm2016 + Score + Electoral.division
##
## Complete :
## (Intercept) mean_tax state.xNSW state.xNSW/ACT
## Electoral.divisionIndi 0 0 0 0
## Electoral.divisionKennedy 0 0 0 0
## Electoral.divisionLyons 0 0 0 0
## Electoral.divisionMayo 0 0 0 0
## Electoral.divisionMelbourne 0 0 0 0
## Electoral.divisionRiverina 0 0 0 0
## Electoral.divisionRyan 0 0 0 0
## Electoral.divisionWentworth 0 0 0 0
## Electoral.divisionWills 1 0 0 0
## state.xNSW/QLD state.xNSW/VIC state.xNT
## Electoral.divisionIndi 0 0 0
## Electoral.divisionKennedy 0 0 0
## Electoral.divisionLyons 0 0 0
## Electoral.divisionMayo 0 0 0
## Electoral.divisionMelbourne 0 0 0
## Electoral.divisionRiverina 0 0 0
## Electoral.divisionRyan 0 0 0
## Electoral.divisionWentworth 0 0 0
## Electoral.divisionWills -1 0 -1
## state.xQLD state.xSA state.xSA/WA/NT
## Electoral.divisionIndi 0 0 0
## Electoral.divisionKennedy 0 0 0
## Electoral.divisionLyons 0 0 0
## Electoral.divisionMayo 0 0 0
## Electoral.divisionMelbourne 0 0 0
## Electoral.divisionRiverina 0 0 0
## Electoral.divisionRyan 0 0 0
## Electoral.divisionWentworth 0 0 0
## Electoral.divisionWills -1 -1 -1
## state.xTAS state.xVIC state.xWA
## Electoral.divisionIndi 0 0 0
## Electoral.divisionKennedy 0 0 0
## Electoral.divisionLyons 1 0 0
## Electoral.divisionMayo 0 0 0
## Electoral.divisionMelbourne 0 0 0
## Electoral.divisionRiverina 0 0 0
## Electoral.divisionRyan 0 0 0
## Electoral.divisionWentworth 0 0 0
## Electoral.divisionWills -1 0 -1
## PartyNm2016Independent
## Electoral.divisionIndi 1
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills -1
## PartyNm2016Katter's Australian Party
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 1
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills 0
## PartyNm2016Liberal
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 1
## Electoral.divisionWills -1
## PartyNm2016Liberal National Party
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 1
## Electoral.divisionWentworth 0
## Electoral.divisionWills 0
## PartyNm2016Nick Xenophon Team
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 1
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills 0
## PartyNm2016The Greens PartyNm2016The Nationals
## Electoral.divisionIndi 0 0
## Electoral.divisionKennedy 0 0
## Electoral.divisionLyons 0 0
## Electoral.divisionMayo 0 0
## Electoral.divisionMelbourne 1 0
## Electoral.divisionRiverina 0 1
## Electoral.divisionRyan 0 0
## Electoral.divisionWentworth 0 0
## Electoral.divisionWills -1 -1
## Score Electoral.divisionAston
## Electoral.divisionIndi 0 0
## Electoral.divisionKennedy 0 0
## Electoral.divisionLyons 0 0
## Electoral.divisionMayo 0 0
## Electoral.divisionMelbourne 0 0
## Electoral.divisionRiverina 0 0
## Electoral.divisionRyan 0 0
## Electoral.divisionWentworth 0 -1
## Electoral.divisionWills 0 0
## Electoral.divisionBallarat
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills -1
## Electoral.divisionBanks
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth -1
## Electoral.divisionWills 0
## Electoral.divisionBarker
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth -1
## Electoral.divisionWills 1
## Electoral.divisionBarton
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills -1
## Electoral.divisionBass
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons -1
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills 0
## Electoral.divisionBatman
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills -1
## Electoral.divisionBendigo
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills -1
## Electoral.divisionBennelong
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth -1
## Electoral.divisionWills 0
## Electoral.divisionBerowra
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth -1
## Electoral.divisionWills 0
## Electoral.divisionBlair
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills 0
## Electoral.divisionBlaxland
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills -1
## Electoral.divisionBonner
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan -1
## Electoral.divisionWentworth 0
## Electoral.divisionWills 0
## Electoral.divisionBoothby
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth -1
## Electoral.divisionWills 1
## Electoral.divisionBowman
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan -1
## Electoral.divisionWentworth 0
## Electoral.divisionWills 0
## Electoral.divisionBraddon
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons -1
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills 0
## Electoral.divisionBradfield
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth -1
## Electoral.divisionWills 0
## Electoral.divisionBrand
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills 0
## Electoral.divisionBrisbane
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan -1
## Electoral.divisionWentworth 0
## Electoral.divisionWills 0
## Electoral.divisionBruce
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills -1
## Electoral.divisionCalare
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina -1
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills 0
## Electoral.divisionCalwell
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills -1
## Electoral.divisionCanberra
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills -1
## Electoral.divisionCanning
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth -1
## Electoral.divisionWills 1
## Electoral.divisionCapricornia
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan -1
## Electoral.divisionWentworth 0
## Electoral.divisionWills 0
## Electoral.divisionCasey
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth -1
## Electoral.divisionWills 0
## Electoral.divisionChifley
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills -1
## Electoral.divisionChisholm
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth -1
## Electoral.divisionWills 0
## Electoral.divisionCook
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth -1
## Electoral.divisionWills 0
## Electoral.divisionCorangamite
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth -1
## Electoral.divisionWills 0
## Electoral.divisionCorio
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills -1
## Electoral.divisionCowan
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills 0
## Electoral.divisionCowper
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina -1
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills 0
## Electoral.divisionCunningham
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills -1
## Electoral.divisionCurtin
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth -1
## Electoral.divisionWills 1
## Electoral.divisionDawson
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan -1
## Electoral.divisionWentworth 0
## Electoral.divisionWills 0
## Electoral.divisionDeakin
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth -1
## Electoral.divisionWills 0
## Electoral.divisionDenison
## Electoral.divisionIndi -1
## Electoral.divisionKennedy 0
## Electoral.divisionLyons -1
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills 1
## Electoral.divisionDickson
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan -1
## Electoral.divisionWentworth 0
## Electoral.divisionWills 0
## Electoral.divisionDobell
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills -1
## Electoral.divisionDunkley
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth -1
## Electoral.divisionWills 0
## Electoral.divisionEden-Monaro
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills -1
## Electoral.divisionFadden
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
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## Electoral.divisionRyan 0 0
## Electoral.divisionWentworth -1 -1
## Electoral.divisionWills 1 1
## Electoral.divisionSydney
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills -1
## Electoral.divisionTangney
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth -1
## Electoral.divisionWills 1
## Electoral.divisionWakefield
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills 0
## Electoral.divisionWannon
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth -1
## Electoral.divisionWills 0
## Electoral.divisionWarringah
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth -1
## Electoral.divisionWills 0
## Electoral.divisionWatson
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills -1
## Electoral.divisionWerriwa
## Electoral.divisionIndi 0
## Electoral.divisionKennedy 0
## Electoral.divisionLyons 0
## Electoral.divisionMayo 0
## Electoral.divisionMelbourne 0
## Electoral.divisionRiverina 0
## Electoral.divisionRyan 0
## Electoral.divisionWentworth 0
## Electoral.divisionWills -1coefs <- coef(model1)
coefs## (Intercept) mean_tax
## 5.69172269093 0.00001806474
## state.xNSW state.xNSW/ACT
## 0.28125382655 0.84366007190
## state.xNSW/QLD state.xNSW/VIC
## 4.67728025050 4.50283781186
## state.xNT state.xQLD
## 3.17872483607 6.56338517491
## state.xSA state.xSA/WA/NT
## 0.48763493055 5.69611598702
## state.xTAS state.xVIC
## -2.16468398837 1.13822502710
## state.xWA PartyNm2016Independent
## 0.26933605575 -4.18885290017
## PartyNm2016Katter's Australian Party PartyNm2016Liberal
## -7.21991293054 -1.33510317717
## PartyNm2016Liberal National Party PartyNm2016Nick Xenophon Team
## -5.59706173390 -3.07277557251
## PartyNm2016The Greens PartyNm2016The Nationals
## -0.83058213195 -0.98311553598
## Score Electoral.divisionAston
## -0.00151685909 1.79483105145
## Electoral.divisionBallarat Electoral.divisionBanks
## -1.67060376832 2.47096202653
## Electoral.divisionBarker Electoral.divisionBarton
## -1.58514520044 0.51172900590
## Electoral.divisionBass Electoral.divisionBatman
## -0.50018040155 0.12878207627
## Electoral.divisionBendigo Electoral.divisionBennelong
## -3.39598208015 1.93667984312
## Electoral.divisionBerowra Electoral.divisionBlair
## 1.42063460268 -6.79866088225
## Electoral.divisionBlaxland Electoral.divisionBonner
## 0.50670872663 -0.04374287351
## Electoral.divisionBoothby Electoral.divisionBowman
## 1.53440226715 -0.10065059926
## Electoral.divisionBraddon Electoral.divisionBradfield
## 2.67953157852 1.01769774266
## Electoral.divisionBrand Electoral.divisionBrisbane
## -0.51378842607 0.24813683546
## Electoral.divisionBruce Electoral.divisionCalare
## -0.55796102164 -0.77721779324
## Electoral.divisionCalwell Electoral.divisionCanberra
## -0.87571191368 0.55222078930
## Electoral.divisionCanning Electoral.divisionCapricornia
## -0.16554414663 -1.61869754892
## Electoral.divisionCasey Electoral.divisionChifley
## 0.05223766358 0.71151409382
## Electoral.divisionChisholm Electoral.divisionCook
## 1.21148609101 2.59353387847
## Electoral.divisionCorangamite Electoral.divisionCorio
## -1.77590697541 -0.27106263298
## Electoral.divisionCowan Electoral.divisionCowper
## 0.19600474110 0.69077945865
## Electoral.divisionCunningham Electoral.divisionCurtin
## 1.24849733325 0.66478754453
## Electoral.divisionDawson Electoral.divisionDeakin
## -1.79593397124 1.74231594187
## Electoral.divisionDenison Electoral.divisionDickson
## 7.22983223107 0.78689431557
## Electoral.divisionDobell Electoral.divisionDunkley
## 1.50397490629 1.50905253856
## Electoral.divisionEden-Monaro Electoral.divisionFadden
## -1.25698003188 0.22214800562
## Electoral.divisionFairfax Electoral.divisionFarrer
## -1.74787826362 -0.41837442347
## Electoral.divisionFisher Electoral.divisionFlinders
## -1.27540117110 -0.66453498735
## Electoral.divisionForde Electoral.divisionForrest
## -0.34509001547 -1.38457690683
## Electoral.divisionFowler Electoral.divisionFranklin
## 0.51790518137 1.37693143472
## Electoral.divisionFremantle Electoral.divisionGellibrand
## -0.74321149361 0.18091366658
## Electoral.divisionGilmore Electoral.divisionGippsland
## 1.47328012074 -2.43603904197
## Electoral.divisionGoldstein Electoral.divisionGorton
## 1.22413008487 0.04103419976
## Electoral.divisionGrayndler Electoral.divisionGreenway
## 1.00975219324 1.48066863282
## Electoral.divisionGrey Electoral.divisionGriffith
## -2.93352435662 -5.63435465720
## Electoral.divisionGroom Electoral.divisionHasluck
## -2.18342115578 1.49629466033
## Electoral.divisionHerbert Electoral.divisionHiggins
## -5.65536627434 1.04220510936
## Electoral.divisionHindmarsh Electoral.divisionHinkler
## -0.03211079727 -2.57405700367
## Electoral.divisionHolt Electoral.divisionHotham
## 0.14238276745 -0.01577400802
## Electoral.divisionHughes Electoral.divisionHume
## 3.04088450412 1.24296953704
## Electoral.divisionHunter Electoral.divisionIndi
## 1.50694756320 NA
## Electoral.divisionIsaacs Electoral.divisionJagajaga
## 0.23529651410 0.17657764709
## Electoral.divisionKennedy Electoral.divisionKingsford Smith
## NA 0.23552749673
## Electoral.divisionKingston Electoral.divisionKooyong
## -0.16931689675 1.14947978581
## Electoral.divisionLa Trobe Electoral.divisionLalor
## 0.28367364953 -0.51821305994
## Electoral.divisionLeichhardt Electoral.divisionLilley
## 0.47527751574 -5.63232444690
## Electoral.divisionLindsay Electoral.divisionLingiari
## 0.91664468033 -5.53857528759
## Electoral.divisionLongman Electoral.divisionLyne
## -5.50631597005 0.11604721538
## Electoral.divisionLyons Electoral.divisionMacarthur
## NA 0.77345261472
## Electoral.divisionMackellar Electoral.divisionMacquarie
## 0.69017294134 -0.67115105116
## Electoral.divisionMakin Electoral.divisionMallee
## 0.70917115655 -3.54108539147
## Electoral.divisionMaranoa Electoral.divisionMaribyrnong
## -3.71510056812 0.15142912027
## Electoral.divisionMayo Electoral.divisionMcEwen
## NA -2.26355212790
## Electoral.divisionMcMillan Electoral.divisionMcPherson
## -1.55387554745 -1.21697114325
## Electoral.divisionMelbourne Electoral.divisionMelbourne Ports
## NA -0.90565170660
## Electoral.divisionMenzies Electoral.divisionMitchell
## 0.88822113541 2.33326381667
## Electoral.divisionMoncrieff Electoral.divisionMoore
## -0.21169680242 1.68586945096
## Electoral.divisionMoreton Electoral.divisionMurray
## -5.86027409571 -3.04471112740
## Electoral.divisionNew England Electoral.divisionNewcastle
## -0.92198865909 0.41528197219
## Electoral.divisionNorth Sydney Electoral.divisionO'Connor
## 0.86741158793 -3.03448323807
## Electoral.divisionOxley Electoral.divisionPage
## -5.31522903256 0.11254907631
## Electoral.divisionParkes Electoral.divisionParramatta
## -0.52380903813 0.80470893826
## Electoral.divisionPaterson Electoral.divisionPearce
## -0.05119115139 -1.03209249032
## Electoral.divisionPerth Electoral.divisionPetrie
## -0.48540400315 0.63688400475
## Electoral.divisionPort Adelaide Electoral.divisionRankin
## 0.05165368108 -5.37614003857
## Electoral.divisionReid Electoral.divisionRichmond
## 1.50346073126 -1.23933097650
## Electoral.divisionRiverina Electoral.divisionRobertson
## NA 1.06778944676
## Electoral.divisionRyan Electoral.divisionScullin
## NA 0.05100751936
## Electoral.divisionShortland Electoral.divisionSolomon
## 1.76805977060 -3.22630004171
## Electoral.divisionStirling Electoral.divisionSturt
## 1.35272095974 1.54032545993
## Electoral.divisionSwan Electoral.divisionSydney
## 1.01220569119 -0.50705914620
## Electoral.divisionTangney Electoral.divisionWakefield
## 1.26778923663 -1.66870538339
## Electoral.divisionWannon Electoral.divisionWarringah
## -2.46568974438 1.16564227173
## Electoral.divisionWatson Electoral.divisionWentworth
## 0.59710726423 NA
## Electoral.divisionWerriwa Electoral.divisionWills
## 0.57048827081 NAHow are the variables affected by one another in our merged dataset? Well, it depends when they are being a nuisance or just confounding. Or plain old collinear. This file shows the very small confounding impacts of some geographic variables on our dependent variable of pc immun class (which categorises the different ranks of % immunisation across Australia). We would expect further modelling to reveal some of the other geographic variables and ABS-related variables to have propensity to confound each other - electorate would have some similarities with SA3s, as geographically they are of a similar size. Postcodes near each other would likely be similar in nature (though possibily not confounding). It would be likely that SEIFA could confound our Demographic variables (though The Vaccinators could not successfully merge the Demographics data (which, like SEIFA is pulled from Census data) to analyse with our other variables). Confounding variables are any other variable in a model that has an effect on your dependent variable. You can see from the simple LM models in this post that there is small confounding impacts on our dependent variable of pc immun class, but not highly significant. Any continuous confounders (as opposed to categorical) could be dealt with by splitting them into brackets or class. Other ways to deal with adjusting variables that ‘interfere’ with each other is to undertake multivariate regression analysis and remove confounding variables stepwise (either forward or back).