Homework 3

Importing Data

Recoding the Variables

1. A binary outcome variable “hlthcare” was defined by dichotomizing “hlthpln1,” a variable from the 2020 BRFSS survey data which measures whether a survey respondent has health care coverage, including health insurance, prepaid plans or government plans.

2. Does access to healthcare coverage vary on the basis of race/ethnicity or education?

3. Two categorical predictor variables were recoded and reveled for this analysis: “race_eth” and “educ.”

Logit/Probit Models & Analysis

sub = brfss20 %>%
  select(hlthcare, race_eth, educ, agec,ins, inc, educ, white, black, hispanic, other, mmsawt, ststr) %>%
  filter( complete.cases( . ))

#Writing in our survey design
options(survey.lonely.psu = "adjust")
des<-svydesign(ids= ~1,
               strata= ~ststr,
               weights= ~mmsawt,
               data = sub )

hlthcare_educ = svyby(formula = ~hlthcare,
           by = ~educ,
           design = des,
           FUN = svymean,
           na.rm=T)

svychisq(~hlthcare+educ,
         design = des)

## 
##  Pearson's X^2: Rao & Scott adjustment
## 
## data:  svychisq(~hlthcare + educ, design = des)
## F = 310.53, ndf = 3.5355e+00, ddf = 5.3643e+05, p-value < 2.2e-16

Plot of Estimates with Standard Errors

As demonstrated by the plots generated below, U.S. adults’ access to healthcare increases as level of education increases. Access to healthcare also varies by race/ethnicity such that NH white adults have the greatest access to healthcare followed by NH other, NH multiracial, and NH Black adults. Hispanic adults have the least access to healthcare.

hlthcare_educ %>%
  ggplot()+
  geom_point(aes(x=educ,y=hlthcare))+
  geom_errorbar(aes(x=educ, ymin = hlthcare-1.96*se, 
                    ymax= hlthcare+1.96*se),
                width=.25)+
   labs(title = "Percent % of US Adults with Access to Healthcare by Education", 
        caption = "Source: CDC BRFSS - SMART Data, 2020 \n Calculations by Christina Quintanilla-Muñoz",
       x = "Education",
       y = "%  Access to Healthcare")+
  theme_minimal()

Race*healthcare Cross Tabulation

hlthcare_race = svyby(formula = ~hlthcare,
           by = ~race_eth, 
           design = des, 
           FUN = svymean,
           na.rm=T)

svychisq(~hlthcare+race_eth,
         design = des)

## 
##  Pearson's X^2: Rao & Scott adjustment
## 
## data:  svychisq(~hlthcare + race_eth, design = des)
## F = 388.54, ndf = 3.5731e+00, ddf = 5.4214e+05, p-value < 2.2e-16

hlthcare_race %>%
  ggplot()+
  geom_point(aes(x=race_eth,y=hlthcare))+
  geom_errorbar(aes(x=race_eth, ymin = hlthcare-1.96*se, 
                    ymax= hlthcare+1.96*se),
                width=.25)+
   labs(title = "Percent % of US  with Access to Healthcare by Race/Ethnicity", 
        caption = "Source: CDC BRFSS - SMART Data, 2020 \n Calculations by Christina Quintanilla-Muñoz",
       x = "Race/Ethnicity",
       y = "%  Access to Healthcare")+
  theme_minimal()

Race by Education by Healthcare Cross Tabulation

The cross tabulation generated below indicates U.S. Hispanic adults have the least access to healthcare across the education gradient, while NH white adults have the greatest access. Across all racial/ethnic groups, within group variability decreases. An interesting pattern emerges for the outcome variable across the “Less than HS” and “Some HS” education categories. Across all racial/ethnic groups, there is greater access to healthcare for adults with the lowest education level than those with some years of high school education.

hlthcare_educ_race = svyby(formula = ~hlthcare,
              by = ~race_eth+educ,
              design = des,
              FUN = svymean,
              na.rm=T)

hlthcare_educ_race %>%
  ggplot()+
  geom_errorbar(aes(x=educ,y = hlthcare,
                    ymin = hlthcare-1.96*se, 
                   ymax= hlthcare+1.96*se,
                   color=race_eth,
                   group=race_eth),
                width=.25,
                position="dodge")+
  labs(title = "Percent % of US  with Access to Healthcare by Race/Ethnicity and Education", 
        caption = "Source: CDC BRFSS - SMART Data, 2020 \n Calculations by Christina Quintanilla-Muñoz",
       x = "Education",
       y = "%  Access to Healthcare")+
  theme_minimal()

Fitting the Logistic Regression Model

#Logit model
fit.logit<-svyglm(hlthcare ~ race_eth + educ + agec,
                  design = des,
                  family = binomial)

## Warning in eval(family$initialize): non-integer #successes in a binomial glm!

summary(fit.logit)

## 
## Call:
## svyglm(formula = hlthcare ~ race_eth + educ + agec, design = des, 
##     family = binomial)
## 
## Survey design:
## svydesign(ids = ~1, strata = ~ststr, weights = ~mmsawt, data = sub)
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           0.79284    0.12662   6.262 3.82e-10 ***
## race_ethhispanic     -1.08964    0.05331 -20.438  < 2e-16 ***
## race_ethnh black     -0.59776    0.06569  -9.099  < 2e-16 ***
## race_ethnh multirace -0.18679    0.13343  -1.400 0.161526    
## race_ethnh other     -0.17364    0.09137  -1.900 0.057389 .  
## educSome HS           0.32913    0.12597   2.613 0.008981 ** 
## educHS grad           1.02307    0.10904   9.382  < 2e-16 ***
## educSome college      1.45948    0.11042  13.217  < 2e-16 ***
## educCollege grad      2.28037    0.11212  20.339  < 2e-16 ***
## agec(24,39]          -0.14998    0.07753  -1.934 0.053054 .  
## agec(39,59]           0.28939    0.07757   3.731 0.000191 ***
## agec(59,79]           1.34008    0.10126  13.234  < 2e-16 ***
## agec(79,99]           2.12464    0.22369   9.498  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1.021851)
## 
## Number of Fisher Scoring iterations: 6

Get Odds Ratios and Confidence Intervals for the Estimates

library(sjPlot)

## Learn more about sjPlot with 'browseVignettes("sjPlot")'.

plot_model(fit.logit,
           axis.lim = c(.1, 10),
           title = "Odds ratios for Access to Health Care")

Probit Model

To get the probit model, you use link = "probit" in svyglm

#probit model
fit.probit<-svyglm(hlthcare~race_eth+educ+agec,
                   design=des,
                   family=binomial(link= "probit"))

## Warning in eval(family$initialize): non-integer #successes in a binomial glm!

Present Both Model Coefficients

library(gtsummary)

## #Uighur

require(rlang)

## Loading required package: rlang

## 
## Attaching package: 'rlang'

## The following objects are masked from 'package:purrr':
## 
##     %@%, as_function, flatten, flatten_chr, flatten_dbl, flatten_int,
##     flatten_lgl, flatten_raw, invoke, splice

t1 = fit.logit%>%
  tbl_regression()

t2 = fit.probit%>%
  tbl_regression()

t_all = tbl_merge(tbls = list(t1, t2))
t_all

Characteristic	Table 1			Table 2
	log(OR)1	95% CI1	p-value	Beta	95% CI1	p-value
race_eth
nh white	—	—		—	—
hispanic	-1.1	-1.2, -1.0	<0.001	-0.59	-0.65, -0.54	<0.001
nh black	-0.60	-0.73, -0.47	<0.001	-0.31	-0.38, -0.25	<0.001
nh multirace	-0.19	-0.45, 0.07	0.2	-0.08	-0.21, 0.05	0.2
nh other	-0.17	-0.35, 0.01	0.057	-0.09	-0.18, 0.00	0.064
educ
Less than HS	—	—		—	—
Some HS	0.33	0.08, 0.58	0.009	0.19	0.04, 0.33	0.011
HS grad	1.0	0.81, 1.2	<0.001	0.59	0.46, 0.71	<0.001
Some college	1.5	1.2, 1.7	<0.001	0.82	0.69, 0.95	<0.001
College grad	2.3	2.1, 2.5	<0.001	1.2	1.1, 1.3	<0.001
agec
(0,24]	—	—		—	—
(24,39]	-0.15	-0.30, 0.00	0.053	-0.08	-0.16, 0.00	0.051
(39,59]	0.29	0.14, 0.44	<0.001	0.16	0.08, 0.24	<0.001
(59,79]	1.3	1.1, 1.5	<0.001	0.67	0.57, 0.77	<0.001
(79,99]	2.1	1.7, 2.6	<0.001	1.0	0.86, 1.2	<0.001
1 OR = Odds Ratio, CI = Confidence Interval

Both of these models show the exact same patterns of effects, with Hispanic, Black, multi-racial, and other race/ethnicity adults showing decreased chances of reporting access to healthcare, when compared to white adults (Reference group).

Similarly, the education variables shows a negative linear trend, with those with more education having higher chances of reporting access to healthcare compared to those with a primary school education (Reference group), and likewise, as people increase in age, they are more likely to report greater access to healthcare, compared to those under age 24 (Reference group).

Fitted Values

library(emmeans)
rg = ref_grid(fit.logit)

marg_logit = emmeans(object = rg,
              specs = c( "race_eth",  "educ", "agec"),
              type="response" )

knitr::kable(marg_logit,  digits = 4)

race_eth	educ	agec	prob	SE	df	asymp.LCL	asymp.UCL
nh white	Less than HS	(0,24]	0.6884	0.0272	Inf	0.6329	0.7390
hispanic	Less than HS	(0,24]	0.4263	0.0302	Inf	0.3685	0.4863
nh black	Less than HS	(0,24]	0.5486	0.0344	Inf	0.4808	0.6147
nh multirace	Less than HS	(0,24]	0.6470	0.0408	Inf	0.5636	0.7224
nh other	Less than HS	(0,24]	0.6500	0.0329	Inf	0.5831	0.7115
nh white	Some HS	(0,24]	0.7544	0.0182	Inf	0.7171	0.7882
hispanic	Some HS	(0,24]	0.5081	0.0259	Inf	0.4574	0.5586
nh black	Some HS	(0,24]	0.6281	0.0268	Inf	0.5742	0.6791
nh multirace	Some HS	(0,24]	0.7181	0.0325	Inf	0.6503	0.7773
nh other	Some HS	(0,24]	0.7208	0.0254	Inf	0.6683	0.7678
nh white	HS grad	(0,24]	0.8601	0.0089	Inf	0.8417	0.8766
hispanic	HS grad	(0,24]	0.6740	0.0189	Inf	0.6359	0.7099
nh black	HS grad	(0,24]	0.7717	0.0158	Inf	0.7393	0.8012
nh multirace	HS grad	(0,24]	0.8360	0.0202	Inf	0.7925	0.8720
nh other	HS grad	(0,24]	0.8378	0.0144	Inf	0.8076	0.8641
nh white	Some college	(0,24]	0.9049	0.0063	Inf	0.8917	0.9165
hispanic	Some college	(0,24]	0.7618	0.0158	Inf	0.7296	0.7913
nh black	Some college	(0,24]	0.8395	0.0124	Inf	0.8138	0.8623
nh multirace	Some college	(0,24]	0.8875	0.0146	Inf	0.8556	0.9131
nh other	Some college	(0,24]	0.8888	0.0105	Inf	0.8665	0.9078
nh white	College grad	(0,24]	0.9558	0.0036	Inf	0.9481	0.9624
hispanic	College grad	(0,24]	0.8791	0.0105	Inf	0.8570	0.8981
nh black	College grad	(0,24]	0.9224	0.0076	Inf	0.9062	0.9360
nh multirace	College grad	(0,24]	0.9472	0.0077	Inf	0.9298	0.9604
nh other	College grad	(0,24]	0.9478	0.0055	Inf	0.9360	0.9576
nh white	Less than HS	(24,39]	0.6554	0.0252	Inf	0.6044	0.7031
hispanic	Less than HS	(24,39]	0.3901	0.0249	Inf	0.3426	0.4398
nh black	Less than HS	(24,39]	0.5113	0.0309	Inf	0.4508	0.5714
nh multirace	Less than HS	(24,39]	0.6121	0.0401	Inf	0.5313	0.6872
nh other	Less than HS	(24,39]	0.6152	0.0323	Inf	0.5503	0.6763
nh white	Some HS	(24,39]	0.7255	0.0163	Inf	0.6924	0.7563
hispanic	Some HS	(24,39]	0.4706	0.0210	Inf	0.4298	0.5118
nh black	Some HS	(24,39]	0.5925	0.0240	Inf	0.5447	0.6385
nh multirace	Some HS	(24,39]	0.6868	0.0326	Inf	0.6196	0.7470
nh other	Some HS	(24,39]	0.6896	0.0256	Inf	0.6374	0.7374
nh white	HS grad	(24,39]	0.8410	0.0070	Inf	0.8269	0.8542
hispanic	HS grad	(24,39]	0.6402	0.0143	Inf	0.6118	0.6677
nh black	HS grad	(24,39]	0.7442	0.0132	Inf	0.7175	0.7693
nh multirace	HS grad	(24,39]	0.8144	0.0209	Inf	0.7700	0.8520
nh other	HS grad	(24,39]	0.8164	0.0147	Inf	0.7857	0.8436
nh white	Some college	(24,39]	0.8911	0.0050	Inf	0.8810	0.9005
hispanic	Some college	(24,39]	0.7335	0.0124	Inf	0.7086	0.7571
nh black	Some college	(24,39]	0.8183	0.0107	Inf	0.7963	0.8384
nh multirace	Some college	(24,39]	0.8716	0.0153	Inf	0.8386	0.8987
nh other	Some college	(24,39]	0.8731	0.0109	Inf	0.8501	0.8930
nh white	College grad	(24,39]	0.9490	0.0026	Inf	0.9437	0.9538
hispanic	College grad	(24,39]	0.8622	0.0078	Inf	0.8461	0.8768
nh black	College grad	(24,39]	0.9110	0.0064	Inf	0.8977	0.9227
nh multirace	College grad	(24,39]	0.9391	0.0079	Inf	0.9216	0.9530
nh other	College grad	(24,39]	0.9399	0.0053	Inf	0.9285	0.9495
nh white	Less than HS	(39,59]	0.7469	0.0207	Inf	0.7043	0.7852
hispanic	Less than HS	(39,59]	0.4981	0.0257	Inf	0.4479	0.5484
nh black	Less than HS	(39,59]	0.6188	0.0285	Inf	0.5616	0.6729
nh multirace	Less than HS	(39,59]	0.7100	0.0345	Inf	0.6380	0.7728
nh other	Less than HS	(39,59]	0.7127	0.0277	Inf	0.6556	0.7638
nh white	Some HS	(39,59]	0.8040	0.0129	Inf	0.7775	0.8280
hispanic	Some HS	(39,59]	0.5797	0.0208	Inf	0.5385	0.6199
nh black	Some HS	(39,59]	0.6929	0.0210	Inf	0.6503	0.7324
nh multirace	Some HS	(39,59]	0.7729	0.0267	Inf	0.7163	0.8210
nh other	Some HS	(39,59]	0.7752	0.0210	Inf	0.7315	0.8136
nh white	HS grad	(39,59]	0.8914	0.0050	Inf	0.8813	0.9008
hispanic	HS grad	(39,59]	0.7341	0.0123	Inf	0.7093	0.7576
nh black	HS grad	(39,59]	0.8187	0.0101	Inf	0.7981	0.8376
nh multirace	HS grad	(39,59]	0.8720	0.0155	Inf	0.8385	0.8993
nh other	HS grad	(39,59]	0.8734	0.0110	Inf	0.8504	0.8934
nh white	Some college	(39,59]	0.9270	0.0034	Inf	0.9200	0.9335
hispanic	Some college	(39,59]	0.8103	0.0099	Inf	0.7901	0.8290
nh black	Some college	(39,59]	0.8748	0.0077	Inf	0.8588	0.8892
nh multirace	Some college	(39,59]	0.9133	0.0108	Inf	0.8896	0.9324
nh other	Some college	(39,59]	0.9144	0.0078	Inf	0.8978	0.9284
nh white	College grad	(39,59]	0.9665	0.0017	Inf	0.9630	0.9697
hispanic	College grad	(39,59]	0.9066	0.0057	Inf	0.8947	0.9173
nh black	College grad	(39,59]	0.9407	0.0043	Inf	0.9317	0.9487
nh multirace	College grad	(39,59]	0.9599	0.0054	Inf	0.9480	0.9692
nh other	College grad	(39,59]	0.9604	0.0036	Inf	0.9526	0.9670
nh white	Less than HS	(59,79]	0.8941	0.0114	Inf	0.8695	0.9145
hispanic	Less than HS	(59,79]	0.7395	0.0226	Inf	0.6929	0.7812
nh black	Less than HS	(59,79]	0.8228	0.0206	Inf	0.7788	0.8595
nh multirace	Less than HS	(59,79]	0.8750	0.0194	Inf	0.8319	0.9083
nh other	Less than HS	(59,79]	0.8765	0.0163	Inf	0.8409	0.9050
nh white	Some HS	(59,79]	0.9214	0.0078	Inf	0.9046	0.9355
hispanic	Some HS	(59,79]	0.7978	0.0183	Inf	0.7596	0.8312
nh black	Some HS	(59,79]	0.8658	0.0153	Inf	0.8328	0.8931
nh multirace	Some HS	(59,79]	0.9068	0.0143	Inf	0.8746	0.9314
nh other	Some HS	(59,79]	0.9079	0.0122	Inf	0.8811	0.9291
nh white	HS grad	(59,79]	0.9591	0.0030	Inf	0.9529	0.9646
hispanic	HS grad	(59,79]	0.8876	0.0087	Inf	0.8694	0.9035
nh black	HS grad	(59,79]	0.9281	0.0068	Inf	0.9136	0.9403
nh multirace	HS grad	(59,79]	0.9512	0.0070	Inf	0.9354	0.9632
nh other	HS grad	(59,79]	0.9518	0.0055	Inf	0.9397	0.9615
nh white	Some college	(59,79]	0.9732	0.0021	Inf	0.9688	0.9770
hispanic	Some college	(59,79]	0.9243	0.0065	Inf	0.9107	0.9361
nh black	Some college	(59,79]	0.9523	0.0049	Inf	0.9418	0.9610
nh multirace	Some college	(59,79]	0.9679	0.0047	Inf	0.9572	0.9760
nh other	Some college	(59,79]	0.9683	0.0038	Inf	0.9599	0.9750
nh white	College grad	(59,79]	0.9880	0.0010	Inf	0.9860	0.9898
hispanic	College grad	(59,79]	0.9652	0.0032	Inf	0.9584	0.9710
nh black	College grad	(59,79]	0.9784	0.0024	Inf	0.9733	0.9826
nh multirace	College grad	(59,79]	0.9856	0.0022	Inf	0.9806	0.9893
nh other	College grad	(59,79]	0.9858	0.0017	Inf	0.9820	0.9888
nh white	Less than HS	(79,99]	0.9487	0.0114	Inf	0.9211	0.9670
hispanic	Less than HS	(79,99]	0.8615	0.0280	Inf	0.7969	0.9079
nh black	Less than HS	(79,99]	0.9105	0.0197	Inf	0.8636	0.9423
nh multirace	Less than HS	(79,99]	0.9388	0.0154	Inf	0.9006	0.9629
nh other	Less than HS	(79,99]	0.9396	0.0142	Inf	0.9051	0.9620
nh white	Some HS	(79,99]	0.9626	0.0079	Inf	0.9435	0.9753
hispanic	Some HS	(79,99]	0.8963	0.0208	Inf	0.8478	0.9306
nh black	Some HS	(79,99]	0.9339	0.0141	Inf	0.9004	0.9567
nh multirace	Some HS	(79,99]	0.9552	0.0110	Inf	0.9281	0.9724
nh other	Some HS	(79,99]	0.9558	0.0101	Inf	0.9313	0.9718
nh white	HS grad	(79,99]	0.9809	0.0040	Inf	0.9712	0.9874
hispanic	HS grad	(79,99]	0.9454	0.0114	Inf	0.9182	0.9639
nh black	HS grad	(79,99]	0.9659	0.0073	Inf	0.9484	0.9776
nh multirace	HS grad	(79,99]	0.9771	0.0056	Inf	0.9630	0.9859
nh other	HS grad	(79,99]	0.9774	0.0051	Inf	0.9648	0.9855
nh white	Some college	(79,99]	0.9876	0.0026	Inf	0.9812	0.9918
hispanic	Some college	(79,99]	0.9640	0.0077	Inf	0.9453	0.9764
nh black	Some college	(79,99]	0.9777	0.0049	Inf	0.9658	0.9855
nh multirace	Some college	(79,99]	0.9851	0.0037	Inf	0.9758	0.9908
nh other	Some college	(79,99]	0.9853	0.0034	Inf	0.9769	0.9906
nh white	College grad	(79,99]	0.9945	0.0012	Inf	0.9916	0.9964
hispanic	College grad	(79,99]	0.9838	0.0036	Inf	0.9751	0.9895
nh black	College grad	(79,99]	0.9900	0.0022	Inf	0.9846	0.9936
nh multirace	College grad	(79,99]	0.9934	0.0017	Inf	0.9891	0.9960
nh other	College grad	(79,99]	0.9935	0.0015	Inf	0.9897	0.9959

In comparing contrived values to the probit model estimates, they are very similar.

rg = ref_grid(fit.probit)

marg_probit = emmeans(object = rg,
              specs = c( "race_eth", "agec"),
              type="response" )
knitr::kable(marg_probit, digits = 4)

race_eth	agec	prob	SE	df	asymp.LCL	asymp.UCL
nh white	(0,24]	0.8516	0.0091	Inf	0.8331	0.8688
hispanic	(0,24]	0.6736	0.0163	Inf	0.6411	0.7048
nh black	(0,24]	0.7671	0.0153	Inf	0.7361	0.7961
nh multirace	(0,24]	0.8318	0.0186	Inf	0.7928	0.8657
nh other	(0,24]	0.8308	0.0138	Inf	0.8024	0.8564
nh white	(24,39]	0.8321	0.0061	Inf	0.8198	0.8438
hispanic	(24,39]	0.6438	0.0109	Inf	0.6222	0.6650
nh black	(24,39]	0.7416	0.0123	Inf	0.7169	0.7651
nh multirace	(24,39]	0.8106	0.0183	Inf	0.7726	0.8443
nh other	(24,39]	0.8095	0.0132	Inf	0.7825	0.8343
nh white	(39,59]	0.8852	0.0045	Inf	0.8761	0.8938
hispanic	(39,59]	0.7283	0.0097	Inf	0.7090	0.7470
nh black	(39,59]	0.8126	0.0099	Inf	0.7926	0.8313
nh multirace	(39,59]	0.8685	0.0144	Inf	0.8381	0.8946
nh other	(39,59]	0.8676	0.0104	Inf	0.8461	0.8869
nh white	(59,79]	0.9567	0.0031	Inf	0.9502	0.9625
hispanic	(59,79]	0.8686	0.0085	Inf	0.8512	0.8846
nh black	(59,79]	0.9192	0.0076	Inf	0.9033	0.9330
nh multirace	(59,79]	0.9486	0.0077	Inf	0.9316	0.9620
nh other	(59,79]	0.9482	0.0063	Inf	0.9347	0.9593
nh white	(79,99]	0.9816	0.0038	Inf	0.9727	0.9879
hispanic	(79,99]	0.9324	0.0115	Inf	0.9069	0.9521
nh black	(79,99]	0.9619	0.0074	Inf	0.9450	0.9743
nh multirace	(79,99]	0.9775	0.0057	Inf	0.9638	0.9865
nh other	(79,99]	0.9773	0.0051	Inf	0.9652	0.9856

The following shows the estimated probability of reporting access to healthcare for each specified type of “typical person” that we generate. Non-Hispanic white adults with a college education are compared Hispanic adults, age 39-59 with a college education:

comps = as.data.frame(marg_logit)

comps[comps$race_eth=="hispanic" & comps$educ == "College grad" , ]

comps[comps$race_eth=="nh white" & comps$educ == "College grad" , ]

Hispanic adults aged 39-59 years demonstrate an estimated probability of reporting access to healthcare of about 90.7%, while the NH white adults of the same age and education level have about a 96.7% chance. This indicates racial/ethnic group has a substantial impact on access to healthcare for U.S. adults.