Relationship Quality

As discussed previously, we split the relationship quality variable into a binary factor of high (\(\equiv 5\)) and low (\(\leq 4\)) on a scale of 1-5. This transformation of sorts serves to fix for the high amount of 5/5 responses observed in the data set. Our intepretation of the relationship quality regression also changes to values of quality.hi representing the probability of a participant claiming a relationship satisfactory rate of 5/5.

This seems like a reasonable model given that we believe that most couples, in general, would like to believe they are as happy as can be in their relationship, unless a particular aspect of their life comes to mind at the asking of the question. This assumption will not only allow us the additional interpretation of significant coefficients serving as penalties that take away from the probability of a participant answering \(\leq 4\).

(!) Note: We have set NA values to 0 along with values 1-4

Next, we would like to compare and isolate 3 different factors (race, religion, and how the couple met) and analyze their individual effect on the probability of a respondent answering high to the relationship quality section of the questionnaire

Respondent’s Race

##                             OR      2.5 %     97.5 %
## (Intercept)       1.782308e+02 103.333345 307.414874
## race.fblack       4.264135e-01   0.120624   1.507398
## race.famer indian 1.763815e+06   0.000000        Inf
## race.fasian pi    1.763814e+06   0.000000        Inf
## race.fOther       1.763815e+06   0.000000        Inf
## race.fHispanic    4.334268e-01   0.140443   1.337616

Likelihood of High Relationship Quality:

Race/Ethnicity	Expression	Value
Black	\(e^{\frac{-0.8523458}{1+e^-0.8523458}}\)	0.5501608
Amer Indian	\(e^{\frac{14.3829894}{1+e^14.3829894}}\)	1.0000082
Asian	\(e^{\frac{14.3829893}{1+e^14.3829893}}\)	1.0000082
Hispanic	\(e^{\frac{-0.8360323}{1+e^-0.83603238}}\)	0.5580871
Other	\(e^{\frac{14.3829894}{1+e^14.3829894}}\)	1.0000082

Analysis: There are a few important things to note about these results.

Respondent’s Religion

##                                         OR      2.5 %     97.5 %
## (Intercept)                   6.483333e+01 28.9485670 145.201008
## religion.fprotestant          5.051414e+00  1.0145590  25.150615
## religion.fcatholic            3.562982e+00  0.8861603  14.325672
## religion.fmormon              4.848833e+06  0.0000000        Inf
## religion.fjewish              4.848833e+06  0.0000000        Inf
## religion.fmuslim              4.848833e+06  0.0000000        Inf
## religion.fhindu               4.848833e+06  0.0000000        Inf
## religion.fbuddhist            4.848833e+06  0.0000000        Inf
## religion.fpentecostal         1.125964e+00  0.1335775   9.491081
## religion.feastern orthodox    4.848833e+06  0.0000000        Inf
## religion.fother christian     1.411311e+00  0.3950837   5.041460
## religion.fother non-christian 6.221080e-01  0.1532812   2.524892
## religion.fnone                7.326478e+00  0.8783182  61.113707

Likelihood of High Relationship Quality:

Religion	Expression	Value
Protestant	\(e^{\frac{1.6196682}{1+e^1.6196682}}\)	1.3068912
Catholic	\(e^{\frac{1.2705978}{1+e^1.2705978}}\)	1.3210908
Mormon	\(e^{\frac{15.3942486}{1+e^15.3942486}}\)	1.0000032
Jewish	\(e^{\frac{15.3942486}{1+e^15.3942486}}\)	1.0000032
Muslim	\(e^{\frac{15.3942486}{1+e^15.3942486}}\)	1.0000032
Hindu	\(e^{\frac{15.3942486}{1+e^15.3942486}}\)	1.0000032
Buddhist	\(e^{\frac{15.3942486}{1+e^15.3942486}}\)	1.0000032
Pentecostal	\(e^{\frac{0.1186396}{1+e^0.1186396}}\)	1.0573915
Eastern Orthodox	\(e^{\frac{15.3942486}{1+e^15.3942486}}\)	1.0000032
Christian Other	\(e^{\frac{0.3445191}{1+e^0.3445191}}\)	1.153587
Non-Christian Other	\(e^{\frac{-0.4746416}{1+e^-0.4746416}}\)	0.7463147
None	\(e^{\frac{1.9914949}{1+e^1.9914949}}\)	1.2702023

Analysis:
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Suspendisse potenti. Nullam venenatis lectus nisi, non commodo nibh rhoncus in. Cras lacus arcu, lobortis elementum urna eget, ultrices tempor nisi. Integer auctor sodales tempus. Etiam finibus mollis orci vel pharetra. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Cras luctus, justo sed venenatis laoreet, orci nisi dignissim eros, non aliquam velit leo eleifend justo. Donec et tristique enim. Aliquam vel nisi arcu. Cras in tortor quis turpis ultrices hendrerit sed quis tellus. Aliquam mattis elit eget sagittis suscipit.

How Couple First Met Partner

##                             OR        2.5 %       97.5 %
## (Intercept)        302.5708170 86.136337385 1.062839e+03
## meet_work            0.4392213  0.105979695 1.820305e+00
## meet_school          0.5370987  0.123119811 2.343043e+00
## meet_church          0.3194061  0.060796180 1.678070e+00
## meet_trip           17.2266758  0.001362569 2.177933e+05
## meet_bar             0.1736482  0.022150570 1.361306e+00
## meet_datingservice   0.4101307  0.089138335 1.887036e+00
## meet_org            21.1522090  0.001438333 3.110656e+05
## meet_party           1.2908395  0.161048660 1.034636e+01
## meet_other           0.4581169  0.121239500 1.731045e+00

Likelihood of High Quality Rating:

Meeting Place	Expression	Value
Work	\(e^{\frac{-0.8228}{1+e^-0.8228}}\)	0.5645849
School	\(e^{\frac{-0.621573}{1+e^-0.621573}}\)	0.6673898
Church	\(e^{\frac{-1.1412919}{1+e^-1.1412919}}\)	0.4210498
Trip	\(e^{\frac{2.8464591}{1+e^2.8464591}}\)	1.1690249
Bar	\(e^{\frac{-1.7507236}{1+e^-1.7507236}}\)	0.2249913
Dating Service	\(e^{\frac{-0.8912793}{1+e^-0.8912793}}\)	0.5314988
Org	\(e^{\frac{3.0517443}{1+e^3.0517443}}\)	1.147703
Party	\(e^{\frac{0.2552928}{1+e^0.2552928}}\)	1.1178875
Other	\(e^{\frac{-0.8228}{1+e^-0.8228}}\)	0.5854531

Analysis:

Our results show that only one of our predictors is significant in the regression of relationship quality on the various ways in which respondents claimed they met their partner throughout. The only significant predictor in this case was met_datingserviceyes. This indicates to us that, the log odds of a person reporting having met via a dating service are

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Overall

## 
## Call:
## glm(formula = quality ~ race.f + inc.f + religion.f + educ + 
##     parentsapproval + married.f, family = "binomial", data = q2set)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.5129   0.0263   0.0719   0.1279   1.0666  
## 
## Coefficients:
##                                 Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                    1.106e+01  2.335e+00   4.736 2.17e-06 ***
## race.fblack                   -2.795e-01  7.652e-01  -0.365  0.71489    
## race.famer indian              1.476e+01  4.590e+03   0.003  0.99743    
## race.fasian pi                 1.465e+01  2.333e+03   0.006  0.99499    
## race.fOther                    1.528e+01  3.736e+03   0.004  0.99674    
## race.fHispanic                 8.467e-02  8.387e-01   0.101  0.91959    
## inc.f                         -5.452e-06  3.827e-06  -1.425  0.15424    
## religion.fprotestant           1.967e+00  1.132e+00   1.738  0.08216 .  
## religion.fcatholic             1.433e+00  9.150e-01   1.567  0.11723    
## religion.fmormon               1.693e+01  2.426e+03   0.007  0.99443    
## religion.fjewish               1.665e+01  2.142e+03   0.008  0.99380    
## religion.fmuslim               1.664e+01  7.429e+03   0.002  0.99821    
## religion.fhindu                1.505e+01  4.990e+03   0.003  0.99759    
## religion.fbuddhist             1.612e+01  3.945e+03   0.004  0.99674    
## religion.fpentecostal         -2.150e-01  1.139e+00  -0.189  0.85034    
## religion.feastern orthodox     1.774e+01  4.837e+03   0.004  0.99707    
## religion.fother christian      5.509e-01  7.376e-01   0.747  0.45509    
## religion.fother non-christian  3.487e-01  9.468e-01   0.368  0.71268    
## religion.fnone                 2.029e+00  1.139e+00   1.782  0.07483 .  
## educ                          -7.635e-02  1.150e-01  -0.664  0.50686    
## parentsapproval               -1.284e+00  2.629e-01  -4.883 1.05e-06 ***
## married.fy                    -2.845e+00  9.009e-01  -3.158  0.00159 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 185.20  on 1927  degrees of freedom
## Residual deviance: 141.78  on 1906  degrees of freedom
##   (1081 observations deleted due to missingness)
## AIC: 185.78
## 
## Number of Fisher Scoring iterations: 19

Analysis

Index

3. Relationship Quality

3a

data <- read.dta('stata.dta')
def='dodgerblue1'

3b

partner = data$qflag

race = data$respondent_race
data["race.f"]=NA
data$race.f=factor(race, labels=c('white','black','amer indian','asian pi','Other','Hispanic'))


educ = data$pp2_respondent_yrsed

inc = as.numeric(data$ppincimp)
data["inc.f"]=NA
for(i in 1:4002){
  data$inc.f[i]=inc[i]
}
data$inc.f[data$inc.f==1] <- 2500
data$inc.f[data$inc.f==2] <- 6250
data$inc.f[data$inc.f==3] <- 8750
data$inc.f[data$inc.f==4] <- 11250
data$inc.f[data$inc.f==5] <- 13750
data$inc.f[data$inc.f==6] <- 17500
data$inc.f[data$inc.f==7] <- 22500
data$inc.f[data$inc.f==8] <- 27500
data$inc.f[data$inc.f==9] <- 32500
data$inc.f[data$inc.f==10] <- 37500
data$inc.f[data$inc.f==11] <- 45000
data$inc.f[data$inc.f==12] <- 55000
data$inc.f[data$inc.f==13] <- 67500
data$inc.f[data$inc.f==14] <- 80000
data$inc.f[data$inc.f==15] <- 92500
data$inc.f[data$inc.f==16] <- 112500
data$inc.f[data$inc.f==17] <- 137500
data$inc.f[data$inc.f==18] <- 162500
data$inc.f[data$inc.f==19] <- 300000

#REMOVED
#age= data$ppage

employ=data$ppwork
data["employ.f"]=NA
data$employ.f=factor(employ)

#REMOVED
#age_met = data$q21a

parentsapproval=data$q30
data["parentsapproval.f"]=NA
data$parentsapproval.f=factor(parentsapproval)

state = data$ppreg4
data["state.f"]=NA
data$state.f=factor(state)

religion = data$papreligion
data["religion.f"]=NA
data$religion.f=factor(religion, labels=c('baptist','protestant','catholic','mormon','jewish','muslim','hindu','buddhist','pentecostal','eastern orthodox','other christian','other non-christian', 'none'))


age_married = data$q21d

married = data$married
data["married.f"]=NA
data$married.f=factor(married, labels=c('n','y'))

marit = data$ppmarit

meet_work = data$q31_1
meet_school = data$q31_2
meet_church = data$q31_3
meet_datingservice = data$q31_4
meet_trip = data$q31_5
meet_bar = data$q31_6
meet_org = data$q31_7
meet_party = data$q31_8
meet_other=data$q31_9

3c

quality=factor(q2set$quality)
quality.num=as.numeric(quality)
hist(quality.num, col=def)
quality.hi = rep(NA, length(quality.num))

for(i in 1:length(quality.hi)){
  if(is.na(quality.num[i]) || quality.num[i]<5){
    quality.hi[i]=0
  }else{
    quality.hi[i]=1
  }
}
quality.hi=factor(quality.hi,levels=c(-1,0,1),labels=c('no response','low','high'))

3d

q2set=data.frame(cbind('race.f'=data$race.f,'educ'=data$pp2_respondent_yrsed,'inc.f'=data$inc.f,'househ'=data$househ,'age_married'=data$age_married,'employ'=data$ppwork,'housing'=data$housing.f,'parentsapproval'=data$parentsapproval.f,'state.f'=data$state.f,'religion.f'=data$religion.f,'relatives'=data$q16), 'quality'=data$relationship_quality,'partner'=data$qflag, 'married.f'=data$married.f,'meet_work'=data$q31_1,'meet_school'=data$q31_2,'meet_church'=data$q31_3,'meet_datingservice'=data$q31_4,'meet_trip'=data$q31_5,'meet_bar'=data$q31_6,'meet_org'=data$q31_7,'meet_party'=data$q31_8,'meet_other'=data$q31_9)

q2set$religion.f = data$religion.f
q2set$race.f = data$race.f
 
meet_work = data$q31_1
q2set$meet_work[meet_work == "refused"] <- NA
q2set$meet_work=as.numeric(meet_work)-2
meet_school = data$q31_2
q2set$meet_school[meet_school == "refused"] <- NA
q2set$meet_school=as.numeric(meet_school)-2
meet_church = data$q31_3
q2set$meet_church[meet_church == "refused"] <- NA
q2set$meet_church=as.numeric(meet_church)-2
meet_trip = data$q31_4
q2set$meet_trip[meet_trip == "refused"] <- NA
q2set$meet_trip=as.numeric(meet_trip)-2
meet_bar = data$q31_5
q2set$meet_bar[meet_bar == "refused"] <- NA
q2set$meet_bar=as.numeric(meet_bar)-2
meet_datingservice = data$q31_6
q2set$meet_datingservice[meet_datingservice == "refused"] <- NA
q2set$meet_datingservice=as.numeric(meet_datingservice)-2
meet_org = data$q31_7
q2set$meet_org[meet_org == "refused"] <- NA
q2set$meet_org=as.numeric(meet_org)-2
meet_party = data$q31_8
q2set$meet_party[meet_party == "refused"] <- NA
q2set$meet_party=as.numeric(meet_party)-2
meet_other = data$q31_9
q2set$meet_other[meet_other == "refused"] <- NA
q2set$meet_other=as.numeric(meet_other)-2

q2set = q2set[which(q2set$partner=='partnered'),]

3e

logit.race = glm(quality~race.f, data=q2set, family='binomial')
summary(logit.race)

## 
## Call:
## glm(formula = quality ~ race.f, family = "binomial", data = q2set)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.2214   0.1058   0.1058   0.1058   0.1617  
## 
## Coefficients:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept)          5.1831     0.2781  18.636   <2e-16 ***
## race.fblack         -0.8523     0.6443  -1.323    0.186    
## race.famer indian   14.3830  1963.4052   0.007    0.994    
## race.fasian pi      14.3830  1376.9103   0.010    0.992    
## race.fOther         14.3830  2032.3174   0.007    0.994    
## race.fHispanic      -0.8360     0.5750  -1.454    0.146    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 240.20  on 2992  degrees of freedom
## Residual deviance: 235.68  on 2987  degrees of freedom
##   (1009 observations deleted due to missingness)
## AIC: 247.68
## 
## Number of Fisher Scoring iterations: 18

3f

coef.race = coefficients(logit.race)
## odds ratios (OR) and 95% CI
exp(cbind(OR = coef(logit.race), confint.default(logit.race)))

3g

logit.religion = glm(quality~religion.f, data=q2set, family='binomial')
summary(logit.religion)

## 
## Call:
## glm(formula = quality ~ religion.f, family = "binomial", data = q2set)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.5115   0.0781   0.0929   0.1474   0.2213  
## 
## Coefficients:
##                                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                      4.1718     0.4114  10.141   <2e-16 ***
## religion.fprotestant             1.6197     0.8190   1.978   0.0480 *  
## religion.fcatholic               1.2706     0.7099   1.790   0.0735 .  
## religion.fmormon                15.3942  1400.0533   0.011   0.9912    
## religion.fjewish                15.3942  1194.8904   0.013   0.9897    
## religion.fmuslim                15.3942  4390.3074   0.004   0.9972    
## religion.fhindu                 15.3942  3104.4162   0.005   0.9960    
## religion.fbuddhist              15.3942  2242.3667   0.007   0.9945    
## religion.fpentecostal            0.1186     1.0876   0.109   0.9131    
## religion.feastern orthodox      15.3942  2982.6266   0.005   0.9959    
## religion.fother christian        0.3445     0.6496   0.530   0.5959    
## religion.fother non-christian   -0.4746     0.7147  -0.664   0.5066    
## religion.fnone                   1.9915     1.0823   1.840   0.0658 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 240.10  on 2985  degrees of freedom
## Residual deviance: 225.35  on 2973  degrees of freedom
##   (1016 observations deleted due to missingness)
## AIC: 251.35
## 
## Number of Fisher Scoring iterations: 18

3h

coef.rel = coefficients(logit.religion)
## odds ratios (OR) and 95% CI
exp(cbind(OR = coef(logit.religion), confint.default(logit.religion)))

3i

logit.how_met = glm(quality~meet_work+meet_school+meet_church+meet_trip+meet_bar+meet_datingservice+meet_org+meet_party+meet_other, data=q2set, family='binomial')
summary(logit.how_met)

## 
## Call:
## glm(formula = quality ~ meet_work + meet_school + meet_church + 
##     meet_trip + meet_bar + meet_datingservice + meet_org + meet_party + 
##     meet_other, family = "binomial", data = q2set)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.1928   0.1108   0.1199   0.1224   0.4482  
## 
## Coefficients:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept)          5.7123     0.6410   8.911   <2e-16 ***
## meet_work           -0.8228     0.7254  -1.134   0.2567    
## meet_school         -0.6216     0.7516  -0.827   0.4082    
## meet_church         -1.1413     0.8464  -1.348   0.1775    
## meet_trip            2.8465     4.8189   0.591   0.5547    
## meet_bar            -1.7507     1.0506  -1.666   0.0956 .  
## meet_datingservice  -0.8913     0.7787  -1.145   0.2524    
## meet_org             3.0517     4.8960   0.623   0.5331    
## meet_party           0.2553     1.0619   0.240   0.8100    
## meet_other          -0.7806     0.6783  -1.151   0.2498    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 240.24  on 2995  degrees of freedom
## Residual deviance: 232.98  on 2986  degrees of freedom
##   (1006 observations deleted due to missingness)
## AIC: 252.98
## 
## Number of Fisher Scoring iterations: 10

3j

coef.hm = coefficients(logit.how_met)
## odds ratios (OR) and 95% CI
exp(cbind(OR = coef(logit.how_met), confint.default(logit.how_met)))

3k

logit.total = glm(quality~race.f+inc.f+religion.f+educ+parentsapproval+married.f, data=q2set, family='binomial')

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

summary(logit.total)

Stat 139 Project

How Couples Meet and Stay Together

Christian Liu, Daniel del Valle, Dion Hagan, Jacob Gollub, and Marina Adario

May 6, 2015