Econometric Analysis of Homelessness in the United States...Econometric Analysis of Homelessness in the United States Ryan Vyskocil Dr. Trees Fall 2015

EconometricAnalysisofHomelessnessintheUnitedStates

RyanVyskocilDr.TreesFall2015

Vyskocil1

Table of Contents

I. Introduction…………………………….……….. 2

II. Equations and Variables……………………….. 3

III. Initial Regression ………………………….…… 5

IV. Second Regressions……………….…………….. 8

V. Analysis………………………………………… 11

VI. Tests of Assumptions: Heteroscedasticity……. 13

VII. Correcting for Heteroscedasticity ……….….. 16

VIII. Tests of Assumptions: Multicollinearity..… 20

IX. Correcting for Heteroscedasticity…………..... 21

X. Tests of Assumptions: Autocorrelation……..... 28

XI. Conclusion…………………………………..…. 29

XII. Appendix……………………………………….. 31

Vyskocil2

I.Introduction Inthisproject,Iamlookingtoanalyzehowstateexpendituresonmental

healthcareaffecttherateofhomelessnesswithineachstate.Iwillbelookingat

2014pointintimeestimatesofhomelessnessintheUnitedStates,andwillbe

analyzingcross-sectionaldatacollectedbystate.Withmydependentvariablebeing

rateofhomelessper10,000personsbystate,themainindependentvariableIwill

beanalyzingismentalhealthcareexpenditurespermentallyillpatient.When

speakingwithnon-profitsintheCapitalRegion,SuchasCaresInc.,Ihavefoundthat

manylocalhomelessnessorganizationsidentifymentalillnessasarootcauseof

homelessness;andwhileIwillbeincludingrateofmentalillnessasacontrol

variableinmyregression,Iamcurioustofindouthowstatespendingonmental

healthcareaffectstherateofhomelessnesswithineachstate.Ihypothesizethat

greaterstatementalhealthcarespendingpermentallyillpersonwilldecreasethe

rateofhomelessnesswithinastate.Moreover,theindependentcontrolvariablesI

willbeanalyzingincludethefollowing:RateofMentalIllness,VeteranPercentage,

UnemploymentRate,StateandLocalWelfareSpendingpercapita,AverageRental

Costs,andFederalRentalAssistancepercapita.IsuspectthatIwillhave

multicollinearitybetweenStateandLocalWelfareandFederalRentalAssistance,so

Iwillruntwoseparateregressions,oneincludingFederalRentalAssistanceasa

control,andoneincludingStateandLocalWelfareSpending.

Vyskocil3

II.EquationandVariablesTheequationsfortheregressionsthatwillberunareasfollows:

HOME=β1+β2MentEx+β3MentRa+β4Vet+β5Rent+β6UnEm+β7FedRent

HOME=β1+β2MentEx+β3MentRa+β4Vet+β5Rent+β6UnEm+β7Welfare

Ho:β2<0

Variable Name Variable Description Data Source Anticipated Slope

Statistical Significant

Practical Significance

HOME

Dependent Variable Data is measured as a rate by state as number of homeless per 10,000 persons (January 2014)

http://www.endhomelessness.org/page/-/files/State_of_Homelessness_2015_FINAL_online.pdf

N/A N/A N/A

MentEx

State Mental Health Agency Mental Health Services Expenditures in millions of dollars/number of mentally ill adults per state (2013)

http://kff.org/other/state-indicator/smha-expenditures/

Negative Significant Medium

MentRa Percentage of Adults with any kind of Mental Illness (2015 report based on data collected in 2012)

http://www.mentalhealthamerica.net/sites/default/files/Parity%20or%20Disparity%202015%20Report.pdf

Positive Significant Medium

Vyskocil4

Variable Name Variable Description Data Source Anticipated Slope

Statistical Significant

Practical Significance

Veteran Veteran Population as a percentage of entire state population (2014)

http://www.va.gov/vetdata/Veteran_Population.asp

Positive Significant High

Rent Average rental cost of a 2 Bedroom Rental Unit at the Fair Market Rate (2014)

https://www.health.ny.gov/diseases/aids/ending_the_epidemic/docs/key_resources/housing_and_supportive_services/out_of_reach_2014.pdf

Positive Significant High

UnEm Rate of unemployment (2014)

http://www.bls.gov/lau/lastrk14.htm

Positive Not Significant Low

Welfare Combined State and Local Welfare Spending/State population (2014)

http://www.usgovernmentdebt.us/compare_state_spending_2015b40a

Positive Not Significant Low

FedRent

Federal Rental Assistance measured is total dollars spent for each state/total population of each state (2014)

http://www.cbpp.org/research/housing/national-and-state-housing-data-fact-sheets?fa=view&id=3586#map

Negative Significant Low

Vyskocil5

III.InitialRegressionsRegressionwithStateandLocalWelfareSpendingasaControl:

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .734a .539 .477

12.1360493952

54902

a. Predictors: (Constant), Unemployment Rate (2014), Rate of Mental Illness (2015 report based on data

from 2011-2012), Mental Health Expenditures per Mentally ill (2013), Rate of Veterans (2014), 2 BR FMR

Average Rental Cost (2014), State and Local Spending per Capita (2014)

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig. B Std. Error Beta

1 (Constant) -81.134 28.855 -2.812 .007

Mental Health Expenditures

per Mentally ill (2013) -.001 .004 -.036 -.267 .790

Rate of Mental Illness (2015

report based on data from

2011-2012)

3.078 1.259 .284 2.446 .019

Rate of Veterans (2014) -.598 1.579 -.047 -.379 .707

2 BR FMR Average Rental

Cost (2014) .032 .010 .446 3.040 .004

State and Local Spending

per Capita (2014) .021 .008 .412 2.449 .018

Unemployment Rate (2014) .449 1.424 .034 .315 .754

a. Dependent Variable: Estimated Homeless per 10,000 (2014)

Vyskocil6

RegressionwithFederalRentalAssistanceasaControl:

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .828a .685 .642 10.03885

a. Predictors: (Constant), Unemployment Rate (2014), Rate of Mental Illness (2015 report based on data

from 2011-2012), Mental Health Expenditures (in millions), Federal Rental Assistance Per Capita (2014),

Rate of Veterans (2014), 2 BR FMR Average Rental Cost (2014)

Afterrunningtheseinitialregressions,manyofthesignsineachofthetwo

runsdidnotmatchmyhypothesizedpredictions.Additionally,manyofthe

independentvariablesthatIpredictedtobestatisticallysignificantwerenot,

includingmentalhealthexpenditures,whichwasthemainindependentvariableI

Coefficientsa

Model


Standardized

Coefficients


1 (Constant) -54.144 24.296 -2.228 .031


(in millions) .000 .002 -.017 -.154 .879



2011-2012)

1.712 1.068 .158 1.603 .116

Rate of Veterans (2014) 1.080 1.538 .084 .702 .486


Cost (2014) .024 .009 .330 2.626 .012

Federal Rental Assistance

Per Capita (2014) .123 .024 .669 5.118 .000

Unemployment Rate (2014) -.647 1.237 -.049 -.523 .604


Vyskocil7

amanalyzing.Ratherthanacceptingthedataandresultsastruthandconcludingmy

initialhypothesiswasincorrect,Idecidedtolookmorecloselyatthedata.

ThefirstthingIdiscoveredwasthattheDistrictofColombia,whichwas

includedinmyinitialregression,isasignificantoutlierthatneedstoberemoved

fromthegroupofobservations.Icametothisconclusionafterlookingatthetwo

scatterplotswhicharedisplayedbelow;WashingtonDChasahomelessnessrate

whichissignificantlygreaterthaneveryotherstateobservation.Additionally,

WashingtonDCreceivesmuchmoreFederalRentalAssistanceandState/Local

Welfarespendingpercapita.Forthesereasons,WashingtonDCwasskewingthe

datatomaketheslopesofeachofthesetwocontrolvariablespositive.If,inreality,

theseslopeswerepositive,thiswouldsignifythatincreasedfederalrental

assistanceandstate/localspendingpercapitaactuallyincreasestherateof

homelessnesswithinastate.

Vyskocil8

Additionally,IrealizedthatthesignificantTvaluesformentalhealth

expendituresineachofthetworegressionsweremuchclosertoonethanIinitially

suspected.Thisledmetobelievethatstatementalhealthcareexpenditureshaveno

effectontherateofhomelessnesswithinastate.BeingthatIamlookingtoprove

thatmentalillnessisinfactarootcauseofhomelessnessandthatstatesshould

spendmoremoneyonmentalhealthcare,IfoundanothervariablethatIdecidedto

includeinmyregression.ThenameofthisvariableisTreatedMI,anditisdescribed

asthepercentageofadultswithamentalillnesswithineachstatethatreceived

somesortoftreatmentoverthepastcalendaryear(MentalHealthAmerica2015).

Inlookingatthisnewvariable,Ihypothesizethatanincreasedpercentageofadults

whoreceivetreatmentfortheirmentalillnesswillinfactdecreasetherateof

homelessnesswithinaState.

IV.SecondRegressionsTheequationsforthenewregressionsthatwillberunwithoutincludingWashingDCasanobservationareasfollows:

HOME=β1+β2MentEx+β3MentRa+β4Vet+β5Rent+β6UnEm+β7FedRent+β8TreatedMI

HOME=β1+β2MentEx+β3MentRa+β4Vet+β5Rent+β6UnEm+β7Welfare+β8TreatedMIHo:β2<0andβ8<0

Vyskocil9

RegressionwithStateandLocalWelfareSpendingasaControl:

Coefficientsa

Model


Standardized

Coefficients


1 (Constant) -15.678 18.738 -.837 .408


per Mentally ill (2013) .000 .002 .030 .218 .828



2011-2012)

1.266 .725 .220 1.746 .088

Rate of Veterans (2014) .904 .881 .126 1.027 .310


Cost (2014) .023 .006 .566 3.605 .001

State and Local Spending

per Capita (2014) .007 .005 .229 1.328 .191

Unemployment Rate (2014) -.797 .838 -.111 -.951 .347

TreatedMI -.470 .198 -.310 -2.374 .022


Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .727a .528 .449

6.66848137092

5258

Vyskocil10

RegressionwithFederalRentalAssistanceasaControl:

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .721a .520 .440

6.72647414831

7498

a. Predictors: (Constant), Federal Rental Assistance Per Capita (2014), TreatedMI, Mental Health

Expenditures per Mentally ill (2013), Rate of Mental Illness (2015 report based on data from 2011-2012),

Unemployment Rate (2014), Rate of Veterans (2014), 2 BR FMR Average Rental Cost (2014)

Coefficientsa

Model


Standardized

Coefficients


1 (Constant) -11.619 19.626 -.592 .557


per Mentally ill (2013) .002 .002 .108 .879 .384



2011-2012)

1.162 .730 .202 1.592 .119

Rate of Veterans (2014) .957 .927 .133 1.032 .308


Cost (2014) .023 .007 .572 3.409 .001

Unemployment Rate (2014) -.976 .912 -.136 -1.070 .291

TreatedMI -.484 .216 -.319 -2.236 .031


Per Capita (2014) .028 .028 .170 1.007 .320


Vyskocil11

Afterrunningeachofthesetworegressions,Idecidedtofocusonthe

regressionthatincludesFederalRentalAssistancepercapitaasacontrolvariable,

ratherthantheregressionthatincludesstateandlocalwelfarespendingpercapita.

Firstofall,Ibelievethatthisindependentvariableisabettercontrolforthemain

independentvariableIamanalyzingbecausefederalrentalassistanceisprovidedto

familiesandindividualsthatcannotaffordtopaytheircurrentmonthlyrent.For

thisreason,onewouldexpecttheamountofassistancepercapitatohaveaneffect

onthenumberofhomelesspersonsinastate,assuchassistanceismeanttokeep

familiesandindividualsoffofthestreetsandinreasonablerentalunits.Moreover,

whileboththefederalrentalassistanceandstate/localspendingpercapitaturned

outtobestatisticallyinsignificant(bothhavingpvalueswellover.05,)the

regressionwithfederalrentalassistanceasacontrolhadagreaterstatistical

significanceofmymainX.Forthesereasons,Ihavedecidedtofocusonthesecond

ofthesetworegressionswhenprovidingmyanalysis.

V.Analysis

TheRSquaredvalueofthisregressionis.520.Thismeansthatthe

independentvariablesinthisregressionexplain52%ofthevariationintherateof

homelessnessamongeachofthestates.Moreover,theonlyindependentvariables

thatarestatisticallysignificantinthisregressionareaveragemonthlyrentalcost

andpercentageofadultswithamentalillnesswhoreceivetreatment;MentalHealth

Vyskocil12

Expenditures,RateofMentalIllness,RateofVeterans,FederalRentalAssistance,

andUnemploymentwereallfoundtobestatisticallyinsignificant.AverageMonthly

rentalcostshasapvalueof.001,andhasaβ5valueof0.023.Thismeansthatfor

everydollarincreaseinastates’averagemonthlyrentalcost,thenumberof

homelesspersonsper10,000peoplewillincreaseby.023.Thisessentiallymeans

thatanincreaseof$44inrentalcostwillresultintherateofhomelessnessinastate

increasingby1person,makingthevariablepracticallysignificant.

Inregardstotheothersignificantindependentvariable,thepercentageof

adultswithamentalillnesswhoreceivetreatment,thepvalueiswithintherangeof

statisticalsignificanceat.031.Thesignofthisvariable’scoefficientisnegative,

signifyingthatthereexistsanegativerelationshipbetweenthepercentageofadults

whohaveamentalillnesswhoreceivetreatmentandtherateofhomelessness

withinastate.Thecoefficientis-0.484,whichtellsusthatforeveryonepercentage

increaseinthepercentageofmentallyilladultswhoreceivetreatment,thenumber

ofhomelesspersonper10,000peoplewilldecreaseby.484.Ibelievethatthis

statisticallyispracticallysignificantaswell,becauseitshowstheimportanceof

treatingmentalillness.Unlikemymainindependentvariable,whichmeasureshow

muchmoneyastatespendsonmentalhealthcarecostspermentallyillperson,this

independentvariablemerelymeasureswhatpercentageofmentallyillpersons

actuallyreceivetreatmentfortheirconditions.

Vyskocil13

VI.TestsofAssumptions:Heteroscedasticity

Initially,IranavisualtestforHeteroscedasticitybysquaringthe

unstandardizedresidualsfrommyregressionandthengraphingthesevaluesina

scatterplotagainsteachofmyindependentvariables.Heteroscedasticityexists

whenanindependentvariableaffectsthespreadofyourresiduals;essentially

meaningthatasthevalueofanindependentvariablechanges,certainvalueranges

oftheindependentvariablehaveasmallerspreadofresidualswhileothershavea

largerspread.Ofallofmyvisualtests,theabovescatterplotwastheonlytestthat

Vyskocil14

seemedtovisuallyexhibitheteroscedasticity.Thisplotdisplaystherelationship

betweentheAverageRentalCostcontrolvariableandthesizeoftheresidual

squared.

Tolookfurtherintothispossibleissue,IthenrantheGlejserTestwhichuses

theabsolutevalueoftheresidualsandmeasuresthecausaleffectofeachvariable

onthisvalue.Inotherwords,theabsolutevalueoftheresidualsbecomethe

dependentvariableintheregressionandthedependentvariablesremainthesame.

Theresultsofthetestcanbeseenbelow.AsIinitiallysuspected,AverageRental

Costsistheonlyvariablethatisstatisticallysignificant,anditseemstoexplain29

percentofthevariationintheresiduals.

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .543a .294 .177 3.74512

a. Predictors: (Constant), TreatedMI, Mental Health Expenditures per Mentally ill (2013), Rate of Veterans

(2014), Unemployment Rate (2014), Rate of Mental Illness (2015 report based on data from 2011-2012), 2

BR FMR Average Rental Cost (2014), Federal Rental Assistance Per Capita (2014)

Vyskocil15

Coefficientsa

Model


Standardized

Coefficients


1 (Constant) -7.663 10.927 -.701 .487


per Mentally ill (2013) .000 .001 -.071 -.479 .635



2011-2012)

-.081 .406 -.031 -.200 .843

Rate of Veterans (2014) .255 .516 .077 .494 .624


Cost (2014) .009 .004 .474 2.330 .025


Per Capita (2014) .011 .015 .152 .741 .463

Unemployment Rate (2014) .252 .508 .076 .497 .622

TreatedMI .043 .120 .061 .354 .725

a. Dependent Variable: RESABSS

IthenusedadifferentequationoftheGlejserTesttoensurethattheAverage

RentalCostsdoesinfactexhibitheteroscedasticity;ratherthanrunningaregression

withmyoriginaldependentvariables,Icalculatedthesquarerootofeach

dependentvariableandranaregressiontoanalyzetheeffectofthesenewvalueson

theresidual.Theresultsareseenbelow.Theaveragerentalcostvariabledoesagain

seemtoexhibitheteroscedasticity,astheRsquarevalueis.294,andthevariable

hasasignificantTvalueof.022.

Vyskocil16

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .542a .294 .196 3.70166

a. Predictors: (Constant), TreatedMISQR, FEDRENTSQR, MentExSqR, RateMISQR, VETSQR, RENTSQR

Coefficientsa

Model


Standardized

Coefficients


1 (Constant) -17.217 19.893 -.865 .392

MentExSqR -.022 .068 -.048 -.319 .752

RateMISQR -.349 3.466 -.015 -.101 .920

VETSQR 11.600 26.343 .067 .440 .662

RENTSQR .556 .234 .476 2.375 .022

FEDRENTSQR .278 .315 .160 .882 .382

TreatedMISQR .229 1.360 .026 .168 .867


VII.CorrectingforHeteroscedasticity

Itisimportanttotryandcorrectforheteroscedasticitybecausethis

conditionmaynegativelyaffecttheRsquarevaluesandstatisticalsignificanceof

variablesintheregression.Inordertocorrectforthisfailedassumption,I

attemptedtotransformthedatabydividingeachvariablebythevalueofthe

variablethatwascausingheteroscedasticity(AverageRentalCosts).Afterdoingthis

Ire-ranmyregressionusingthesenewvalues,andtheresultsmaybeseenbelow.

Vyskocil17

Model Summaryb

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .393a .154 .013 .00668

a. Predictors: (Constant), Rent2, MentEx2, FedRent2, UnEm2, Vet2, TreatedMI2, MentRa2

b. Dependent Variable: HOME2

Coefficientsa

Model


Standardized

Coefficients


1 (Constant) .025 .006 3.892 .000

MentEx2 .002 .002 .152 .989 .328

MentRa2 .702 .625 .586 1.124 .267

Vet2 1.160 .855 .448 1.356 .182

FedRent2 .008 .024 .056 .335 .739

UnEm2 -.661 .731 -.188 -.904 .371

TreatedMI2 -.264 .182 -.521 -1.456 .153

Rent2 -15.472 14.940 -.561 -1.036 .306

a. Dependent Variable: HOME2

Wemustthenre-runourtestsforheteroscedasticityinordertodetermineif

wedidinfactcorrectfortheissuethatwasaffectingourdata.Inordertodothis,I

re-rantheGlejserTestusingthenewabsolutevaluesoftheregressionrunwiththe

transformeddata.Theresultsofthetestmaybeseenbelow.

Vyskocil18

Model Summaryb

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .451a .203 .070 .0038627

a. Predictors: (Constant), Rent2, MentEx2, FedRent2, UnEm2, Vet2, TreatedMI2, MentRa2

b. Dependent Variable: RESABS2

Coefficientsa

Model


Standardized

Coefficients


1 (Constant) .013 .004 3.363 .002

MentEx2 .000 .001 -.038 -.254 .801

MentRa2 -.093 .361 -.131 -.259 .797

Vet2 .377 .494 .244 .762 .450

FedRent2 .008 .014 .093 .571 .571

UnEm2 -.044 .422 -.021 -.105 .917

TreatedMI2 -.040 .105 -.132 -.381 .705

Rent2 -6.376 8.633 -.388 -.739 .464

a. Dependent Variable: RESABS2

Afterrunningthistest,itappearsthatheteroscedasticityisstillaffectingthe

transformeddata.Thisisbecauseoncewemultiplytheinitialproblematicvariable

(AverageRentalCosts)backthroughtheentireequation,thebetaandsignificance

valuesfortheconstantbecomethevaluesthatsignifyslopeandstatistical

significancefortheoriginalproblematicvariable(AverageRentalCosts).Thisbeing

thecase,thesignificantTvalueforthisindependentvariableis.002meaningthatit

isstillstatisticallysignificantinexplainingthevariationintheresiduals.Fromhere,

itstartstobecomeclearthatheteroscedasticityinthiscasemaynotbecorrectable;

Vyskocil19

wemaythereforehavetoacceptthelowlevelofheteroscedasticitypresentinour

initialregression.Ascanbeseenbelow,theRenalCostvariableonlyaccountsfor

26.5%ofthevariationintheresidual;whilethisisnotanidealsituation,Idonot

believethatthiscaseofheteroscedasticityissevereenoughtodiscardtheresultsof

theregressionandremovethevariablefromourequation.

Model Summaryb

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .515a .265 .250 3.57586

a. Predictors: (Constant), 2 BR FMR Average Rental Cost (2014)

b. Dependent Variable: RESABSS

Coefficientsa

Model


Standardized

Coefficients


1 (Constant) -3.863 2.101 -1.839 .072


Cost (2014) .010 .002 .515 4.159 .000


Vyskocil20

VIII.TestsofAssumptions:Multicollinearity

Afterrunningdifferenttestsonmydata,someofmyvariablesdoseemto

exhibitsignsofbeingmulticollinear,meaningthatsomeofmyvariablesmove

togetherinastraightlinerelationship.Theeasiestwaytoidentifymulticollinearity

istocreateaPearsonCorrelationtableonSPSSwhilerunningaregression.Bydoing

this,oneisabletoidentifythecorrelationrelationshipbetweeneachsetof

variables.Thevaluesinthetablerangefrom0-1,with0signifyingthatabsolutelyno

multicollinearityispresent,and1signifyingthatthevariablesmovetogether

exactly.Inclass,weidentifiedanyvariablewithaPearsonCorrelationvaluegreater

Correlations

Estimated

Homeless

per

10,000

Mental

Health

Expenditures

per Mentally

ill

Rate of

Mental

Illness

Rate of

Veterans

2 BR FMR

Average

Rental

Cost

Federal

Rental

Assistance

Per Capita

Unempl

oyment

Rate

Treated

Mentally

Ill

Pearson

Correlation

Estimated Homeless per

10,000 1.000 .289 -.142 -.091 .648 .337 .078 -.350


per Mentally ill .289 1.000 -.259 -.014 .391 .304 .033 .112

Rate of Mental Illness -.142 -.259 1.000 .353 -.462 -.269 .014 .159

Rate of Veterans -.091 -.014 .353 1.000 -.331 -.444 -.171 .165


Cost .648 .391 -.462 -.331 1.000 .575 .134 -.288


Per Capita .337 .304 -.269 -.444 .575 1.000 .290 .134

Unemployment Rate .078 .033 .014 -.171 .134 .290 1.000 -.327

TreatedMI -.350 .112 .159 .165 -.288 .134 -.327 1.000

Vyskocil21

than.3asatriskofexhibitingmulticollinearity.Alloftherelationshipsbetween

variablesthatfallabovethis.3thresholdarehighlightedabove.Ofthe21variable

relationshipsthatcouldexhibitmulticollinearity,8ofthecorrelationvaluesfall

withinthisthreshold,butnonfallabovethevalueof.6whichwouldindicatethat

thereisstrongmulticollinearitywhichisskewingmydata.

TheexistenceofmulticollinearityinmyregressionwillnotaffectmyR

squarevalue,whichwas.520,butitmayverywellaffectthesignificancevalues(t

statandsignificanttvalue);itisthereforeimportantthatwetransformourdatain

ordertocorrectformulticollinearityinthedata.

IX.CorrectingforMulticollinearityAfteranalyzingthedifferentcasesofmulticollinearitythatmyvariables

exhibit,Iconcludedthattotransformthedata,Iwouldhavetocompletelychange

thescopeofmyvariables;Ibelievethatthiswoulddomoreharmtothestorythan

good,soIchosetonottransformanyvariables.Ratherthanthisapproach,Ibegan

topulldifferentvariablesfrommyregressiontoseewhatresultsdifferent

combinationsofvariablesyielded.Firstoff,IremovedtheFederalRentalAssistance

variablefrommyregression;theresultsareseenbelow.Indoingso,myRsquare

remainedhighat.508andthesametwovariables,percenttreatmentofmental

illnessandaveragerentalcosts,remainedstatisticallysignificant.Theonly

differencebetweenmylastregressionandthisoneisthatthesignificanceofthe

rateofmentalillnessindependentvariableincreasedsignificantly(pvalueof.111),

butitdidnotincreaseenoughtoconsiderthevariablestatisticallysignificant.

Vyskocil22

Additionally,almostallmulticollinearitywasremovedfrommyregression.Theonly

variablethatcontinuestoconsistentlydisplaymulticollinearityistheaveragerental

costvariable,asitseemstobecollinearwithMentalHealthExpenditures,Rateof

MentalIllness,andtheRateofVeterans.

Coefficientsa

Model


Standardized

Coefficients


1 (Constant) -17.039 18.875 -.903 .372


per Mentally ill (2013) .002 .002 .112 .915 .365



2011-2012)

1.188 .729 .207 1.629 .111

Rate of Veterans (2014) .609 .860 .085 .708 .483


Cost (2014) .027 .006 .669 4.866 .000

Unemployment Rate (2014) -.600 .832 -.083 -.721 .475

TreatedMI -.371 .185 -.244 -2.005 .051


Model Summary

Model R R Square Adjusted R Square Std. Error of the Estimate

1 .713a .508 .440 6.727503856277718

a. Predictors: (Constant), TreatedMI, Mental Health Expenditures per Mentally ill (2013), Rate of Veterans (2014), Unemployment Rate (2014), Rate of Mental Illness (2015

report based on data from 2011-2012), 2 BR FMR Average Rental Cost (2014)

Vyskocil23

Correlations

Estimated

Homeless

per 10,000

Mental Health

Expenditures

per Mentally ill

Rate of

Mental

Illness

Rate of

Veterans

2 BR FMR

Average

Rental Cost

Unemploy

ment Rate

Treated

MI

Pearson

Correlation

Estimated Homeless

per 10,000 1.000 .289 -.142 -.091 .648 .078 -.350

Mental Health

Expenditures per

Mentally ill

.289 1.000 -.259 -.014 .391 .033 .112

Rate of Mental

Illness -.142 -.259 1.000 .353 -.462 .014 .159

Rate of Veterans -.091 -.014 .353 1.000 -.331 -.171 .165

2 BR FMR Average

Rental Cost .648 .391 -.462 -.331 1.000 .134 -.288

Unemployment Rate .078 .033 .014 -.171 .134 1.000 -.327

TreatedMI -.350 .112 .159 .165 -.288 -.327 1.000

NextIdecidedtoremovetheAverageRentalCostvariablefrommy

regressiontoseehowtheresultsmaybeaffected.Realistically,itisnotidealto

removetwovariablesfrommyregressionbecauseitisimportanttohaveenough

controlvariablestopaintanaccuratepictureofhowthemainindependentvariable

affectsthedependentvariable,butIwascuriousastohowthisremovalwouldaffect

myregression.Theresultsareseenbelow.TheRsquarevaluedecreasesto.237and

thepvalueofmymainindependentvariable,mentalhealthexpenditures,decreases

to.017,makingthevariablestatisticallysignificant;howeverthesignonthis

variableispositive,whichistheoppositeofmyinitialhypothesis.Thisresultmeans

thatasforevery$1increaseinmentalhealthcareexpenditurespermentallyill

Vyskocil24

patient,thenumberofhomelesspersonsactuallyincreasesby.005perevery

10,000people.Thisbetavalueisnot,inmyopinion,practicallysignificantthough

becauseitwouldmeanthattherateofhomelessnessinastatewouldonlyincrease

by1personforevery10,000peopleasaresultofeveryadditional$200spenton

eachindividualmentallyillperson.Also,multicollinearityisalmostnonexistentin

thisregression,withonlytwoPearsonCorrelationvaluesslightlyabovetheof0.3

targetvalue.

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .487a .237 .151

8.28161322218

2546

a. Predictors: (Constant), TreatedMI, Mental Health Expenditures per Mentally ill (2013), Rate of Veterans

(2014), Unemployment Rate (2014), Rate of Mental Illness (2015 report based on data from 2011-2012)

Coefficientsa

Model


Standardized

Coefficients


1 (Constant) 40.352 18.141 2.224 .031


per Mentally ill (2013) .005 .002 .344 2.472 .017



2011-2012)

.162 .860 .028 .189 .851

Rate of Veterans (2014) -.295 1.034 -.041 -.286 .777

Unemployment Rate (2014) -.539 1.024 -.075 -.527 .601

TreatedMI -.624 .218 -.411 -2.856 .007


Vyskocil25

Correlations

Estimated

Homeless

per 10,000

Mental Health

Expenditures

per Mentally ill

Rate of

Mental

Illness

Rate of

Veterans

Unemploym

ent Rate

Treated

MI

Pearson

Correlation

Estimated Homeless per

10,000 1.000 .289 -.142 -.091 .078 -.350


per Mentally ill .289 1.000 -.259 -.014 .033 .112

Rate of Mental Illness -.142 -.259 1.000 .353 .014 .159

Rate of Veterans -.091 -.014 .353 1.000 -.171 .165

Unemployment Rate .078 .033 .014 -.171 1.000 -.327

TreatedMI -.350 .112 .159 .165 -.327 1.000

FinallyIdecidedtoreintroducetheFederalRentalAssistancevariableinto

myregression,whilecontinuingtoleaveouttheAverageRentalCostvariable.The

resultsareseenbelow.TheRsquareofthisregressionis.387andtheonlytwo

variablesthatarestatisticallysignificantarethepercentageofadultswithamental

illnesswhoreceivetreatmentandthefederalrentalassistancepercapita.Mymain

independentvariableisonceagainveryclosetobeingstatisticallysignificant,.083,

butremainspracticallyinsignificantwithabetavalueof.003.TheFederalRental

Assistancevariableisstatisticallysignificantwithapvalueof.002,andhasabeta

valuesof.081.Thismeansthatforevery$1increaseinFederalRentalAssistance

percapita,thenumberofhomelesspersonsper10,000peopleincreasesby.081.

Thisvaluedefinitelyhassomesortofpracticalsignificancebecauseitmeansthat

thenumberofhomelesspersonsincreasebyonepersonforevery$12.34increase

inFederalRentalAssistancepercapitawithinastate.Moreimportantly,the

Vyskocil26

variabledescribingthepercentageofadultswithamentalillnesswhoreceive

treatmentisverystatisticallyandpracticallysignificant.WithaTstatisticof4.043,

thisvariableismostdefinitelystatisticallysignificantwithintheregression;and

withabetavalueof-.848,wecanconcludethatforeverypercentageincreaseinthe

numberofmentallyilladultswhoreceivetreatment,thenumberofhomeless

personsper10,000decreasesby.848,whichisnearlyoneperson.Beingthatthe

meanofallofmyobservationsis18.03homelesspersonsper10,000people,a

decreaseofnearlyonepersonforeveryonepercentageincreaseintreatmentof

adultmentalillnessisaverysignificantfinding.Also,multicollinearityisnotvery

prevalentinthisregression,withonlyfourPearsonCorrelationvaluesslightly

abovethecuspof0.3.

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .622a .387 .301

7.51141552270

3936

a. Predictors: (Constant), Federal Rental Assistance Per Capita (2014), TreatedMI, Mental Health

Expenditures per Mentally ill (2013), Rate of Mental Illness (2015 report based on data from 2011-2012),

Unemployment Rate (2014), Rate of Veterans (2014)

Vyskocil27

Coefficientsa

Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) 31.841 16.662 1.911 .063

Mental Health Expenditures per

Mentally ill .003 .002 .233 1.777 .083

Rate of Mental Illness .522 .787 .091 .663 .511

Rate of Veterans 1.113 1.033 .155 1.077 .288

Unemployment Rate -1.672 .993 -.232 -1.684 .099

TreatedMI -.848 .210 -.560 -4.043 .000

Federal Rental Assistance Per

Capita .081 .025 .501 3.238 .002


Correlations

Estimated

Homeless

per 10,000

Mental Health

Expenditures

per Mentally ill

Rate of

Mental

Illness

Rate of

Veteran

Unempl

oyment

Rate

Treated

MI

Federal Rental

Assistance

Per Capita

Pearson

Correlation

Estimated Homeless

per 10,000 1.000 .289 -.142 -.091 .078 -.350 .337

Mental Health

Expenditures per

Mentally ill

.289 1.000 -.259 -.014 .033 .112 .304

Rate of Mental Illness -.142 -.259 1.000 .353 .014 .159 -.269

Rate of Veterans -.091 -.014 .353 1.000 -.171 .165 -.444

Unemployment Rate .078 .033 .014 -.171 1.000 -.327 .290

TreatedMI -.350 .112 .159 .165 -.327 1.000 .134

Federal Rental

Assistance Per Capita .337 .304 -.269 -.444 .290 .134 1.000

Vyskocil28

X.TestsofAssumptions:Autocorrelation

Model Summaryb

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate Durbin-Watson

1 .721a .520 .440

6.72647414831

7500 2.167

a. Predictors: (Constant), TreatedMI, Mental Health Expenditures per Mentally ill (2013), Rate of Veterans (2014), Unemployment Rate

(2014), Rate of Mental Illness (2015 report based on data from 2011-2012), 2 BR FMR Average Rental Cost (2014), Federal Rental

Assistance Per Capita (2014)

b. Dependent Variable: Estimated Homeless per 10,000 (2014)

NormallyAutocorrelationisnotanissueforcomplexregressionsrunusing

cross-sectionaldata,butitisstillnecessarytotestforthisassumptiontoensurethat

itisnotaffectingmydata.Todoso,IselectedtocalculatetheDurbin-Watson

statisticwhenIranmyinitialregressiononSPSS.Asisdisplayedabove,myDurbin-

Watsonvalueis2.167.Thisvaluecanrangefrom0-4,andthecloseritistotwo,the

moresurewearethatautocorrelationisnotaffectingthedata.Initially,beingthat

thestatisticis2.167,wecanbefairlycertainthatthedatadoesnotexhibit

autocorrelation,buttoensurethatthisistrue,wemustcreateaDurbin-Watsond

statisticchartandplotourstatisticwithinoneoftherangesofthischart.TodothisI

usedmynumberofobservationsandnumberofindependentvariablesalongwitha

Durbin-Watsoncriticalvaluecharttofindmydlanddustatistics.Aftercalculating

thesevaluesandcreatingthechartbelow,itisclearthatthedatadoesnotexhibit

autocorrelation,astheDurbin-Watsonstatisticabove,2.167,fallsinthemiddle

regionofthechart.Thissignifiesthatautocorrelationisnotpresent.

Vyskocil29

XI.Conclusions Afteranalyzingthecollecteddatausingeconometrictechniques,afew

differentconclusionscanbemade.Firstandforemost,thedatausedforthisreport

isdefinitelynotthestrongestdatatoanalyzetheeffectofmentalhealth

expendituresonhomelessness.Theidealmeansofanalyzingmyhypothesiswould

betoanalyzehomelessnessdatacollectedbyfiftycitiesthroughouttheUnited

States,butaggregatingthissortofdatawassimplyunrealisticconsideringthescope

ofandresourcesavailableforthisreport.

Moreover,itmaybeconcludedthattheamountofmoneyastatespendson

mentalhealthcarepermentallyillpatientdoesnotexplainanyvariationintherate

ofhomelessnesswithinastate.Thatbeingsaid,itisveryclearthatthepercentageof

adultswithamentalillnesswhoactuallyreceivetreatmentfortheirillnessdoes

significantlyaffecttherateofhomelessnesswithinastate.Ibelievethatthisspeaks

Vyskocil30

volumesabouthowweapproachmentalillnessintheUnitedStates.Whilethis

reportonlydealswithhowmentalillnessaffectshomelessness,itisclearthatpolicy

solutionsthatdealwithmentalillnessmustbemostfocusedondiagnosingand

reachingalladultsthathaveamentalillness.Todothis,programsmustbefocused

oneducatingthepublicregardingtheimportanceoftreatment,andmustgobeyond

simplyincreasingfundingtomentalhealthcareprogramsthatareinefficientin

termsofreachingalargeportionofthepopulation.

Furthermore,althoughthevariablewasbothheteroscedasticandcollinear

withmultiplevariables,itseemsthatAverageRentalCostsplayalargerolein

determiningtherateofhomelessnesswithinagivenstate.Beingthatinevery

regressionthisvariablehadasignificantTstatandaccountedforalargepartofthe

Rsquarevalue,itmaybeconcludedthatthemaincauseofhomelessnessinthe

UnitedStatesseemstobepurelyeconomicinnature.Beingthatthisvariableis

practicallysignificant,withhomelesspersonper10,000peopleincreasingbyone

personforevery$44increaseinaveragerent,itbecomesclearthatalargepartof

whatiscausingpeopletobehomelessintheUnitedStatesisthattheyeitherlacka

streamofincome,ordonothavealargeenoughstreamofincometoaffordrental

costswithintheirregionofthenation.Homelessnessisaverydifficulttopicto

understandduetothemanydifferentperceivedcausesofhomeless;butitis

importantthatreportslikethesearedonebecausealthoughhomelessnessaffectsa

verysmallpercentageofthenation,itisapressingpublicproblemthatneedstobe

addressedinmanyregionsofthenation.

Vyskocil31

XII.Appendix

EstimatedHomelessper10,000(2014)

MentalHealthExpendituresperMentallyill(2013)

RateofMentalIllness(2015reportbasedondatafrom2011-2012)

RateofVeterans(2014)

2BRFMRAverageRentalCost(2014)

FederalRentalAssistancePerCapita(2014)

StateandLocalSpendingperCapita(2014)

UnemploymentRate(2014)

Percentageofadultswithanymentalillnesswhoreceivedtreatment(2015reportbasedondatafrom2011-2012)

ALABAMA 9.41 $501.43 19.32 8.53% $683.00 $111.15 $371.18 6.8 40.3ALASKA 24.22 $2,500.52 18.94 9.96% $1,125.00 $95.01 $1,628.81 6.8 36.2ARIZONA 15.59 $1,504.77 18.83 7.91% $911.00 $47.98 $415.96 6.9 37.6ARKANSAS 9.90 $311.44 19.81 8.40% $653.00 $81.24 $471.96 6.1 46.2CALIFORNIA 29.37 $1,234.28 17.68 4.77% $1,354.00 $130.58 $1,172.60 7.5 35.7COLORADO 18.72 $744.79 18.12 7.72% $916.00 $79.91 $597.48 5 41.5CONNECTICUT 12.37 $1,701.75 16.71 5.93% $1,197.00 $206.30 $1,056.53 6.6 46.5DELAWARE 9.63 $706.21 18.26 8.35% $1,044.00 $115.43 $748.17 5.7 47.8DC 117.59 $1,994.24 19.44 4.53% $1,469.00 $632.88 $1,973.01 7.8FLORIDA 20.88 $150.61 19.87 7.96% $1,008.00 $77.16 $417.23 6.3 35.4GEORGIA 16.36 $433.18 18.99 7.46% $809.00 $96.46 $475.37 7.2 34.8HAWAII 48.73 $998.88 17.48 8.52% $1,640.00 $138.78 $774.89 4.4 26.5IDAHO 12.87 $224.26 20.58 8.10% $692.00 $52.00 $428.27 4.8 47.9ILLINOIS 10.18 $610.83 15.86 5.60% $902.00 $150.54 $931.64 7.1 42.7INDIANA 9.05 $482.98 19.87 7.22% $729.00 $77.16 $606.35 6 41.1IOWA 10.05 $1,037.26 18.4 7.46% $689.00 $63.08 $514.95 4.4 44.3KANSAS 9.58 $944.88 18.2 7.62% $746.00 $60.95 $516.53 4.5 49.9KENTUCKY 11.53 $379.37 19.47 7.49% $660.00 $104.00 $589.11 6.5 45.6LOUISIANA 9.91 $393.78 19.28 7.10% $804.00 $135.06 $516.16 6.4 35.9MAINE 20.49 $2,182.25 20.05 9.57% $842.00 $165.40 $827.01 5.7 50.1MARYLAND 13.15 $1,332.33 17.93 7.32% $1,297.00 $162.14 $937.02 5.8 43MASSACHUSETTS 31.48 $826.20 17.38 5.63% $1,252.00 $278.86 $1,349.07 5.8 52.7MICHIGAN 12.34 $867.18 19.81 6.64% $748.00 $83.55 $736.64 7.3 42.5MINNESOTA 15.35 $1,392.69 17.18 6.76% $856.00 $94.55 $989.52 4.1 45.3MISSISSIPPI 7.43 $378.98 20.27 7.36% $707.00 $119.90 $434.19 7.8 34.9MISSOURI 12.01 $2,548.13 18.99 8.15% $744.00 $85.26 $412.30 6.1 44.8MONTANA 17.05 $1,453.17 18.92 9.74% $705.00 $67.41 $683.87 4.7 46.1NEBRASKA 16.08 $687.65 17.89 7.62% $701.00 $71.75 $744.09 3.3 51NEVADA 37.18 $759.57 16.05 8.03% $1,001.00 $70.80 $634.00 7.8 30.9NEWHAMPSHIRE 10.37 $963.00 18.53 8.57% $1,049.00 $131.14 $753.69 4.3 49.8NEWJERSEY 13.06 $1,891.25 14.66 4.79% $1,296.00 $170.06 $1,208.30 6.6 36.9NEWMEXICO 13.17 $827.00 19.59 8.22% $774.00 $71.44 $527.43 6.5 43.9NEWYORK 40.81 $1,833.20 18.61 4.52% $1,293.00 $274.74 $1,149.59 6.3 38.9NORTHCAROLINA 11.56 $779.54 16.84 7.79% $747.00 $79.65 $683.83 6.1 45.4NORTHDAKOTA 17.01 $703.78 17.21 7.76% $738.00 $75.73 $676.15 2.8 38.7OHIO 10.20 $678.43 19.64 7.47% $720.00 $122.65 $853.88 5.7 47.4OKLAHOMA 10.81 $333.33 21.88 8.70% $689.00 $73.49 $489.94 4.5 41.5OREGON 30.64 $1,156.89 20.89 8.35% $846.00 $90.67 $856.37 6.9 44.7PENNSYLVANIA 11.99 $2,077.34 17.99 7.34% $901.00 $120.28 $1,024.46 5.8 48RHODEISLAND 11.28 $721.62 18.8 6.82% $928.00 $274.84 $1,137.25 7.7 46.4SOUTHCAROLINA 10.46 $401.45 19.56 8.64% $756.00 $80.91 $393.17 6.4 46.8SOUTHDAKOTA 10.37 $655.46 17.77 8.44% $680.00 $78.53 $586.05 3.4 47TENNESSEE 14.38 $578.65 20.25 7.73% $729.00 $92.22 $534.40 6.7 43.4TEXAS 10.57 $344.68 16.86 6.23% $872.00 $66.74 $385.80 5.1 36.1UTAH 10.47 $476.11 22.35 5.16% $794.00 $42.14 $509.70 3.8 43.2VERMONT 24.88 $1,902.08 19.39 7.76% $1,007.00 $159.60 $1,117.21 4.1 57.1VIRGINIA 8.43 $709.32 17.5 9.38% $1,088.00 $92.84 $588.50 5.2 51.3WASHINGTON 26.12 $732.31 20.77 8.55% $970.00 $99.84 $764.71 6.2 44.4WESTVIRGINIA 10.88 $568.19 21.88 9.04% $665.00 $92.96 $540.45 6.5 47.7WISCONSIN 10.52 $834.06 17.98 7.19% $767.00 $66.69 $851.05 5.5 41.3WYOMING 12.96 $819.54 19.6 8.51% $768.00 $58.20 $513.56 4.3 40

Documents

Econometric Analysis of Homelessness in the United States...Econometric Analysis of Homelessness in the United States Ryan Vyskocil Dr. Trees Fall 2015