Homework Assignment 3

Perform a logistic regression (or probit regression) of a binary outcome, using the dataset of your choice. I ask you specify a research question for your analysis and generate appropriate predictors in order to examine your question.

Research Question: Do those who report having no health coverage or having a recent check up less likely to report poor health?

fit.logit<-svyglm(badhealth ~ sex + hlthpln1 + checkup1,
                  design = des,
                  family = binomial)

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

summary(fit.logit)

## 
## Call:
## svyglm(formula = badhealth ~ sex + hlthpln1 + checkup1, design = des, 
##     family = binomial)
## 
## Survey design:
## svydesign(ids = ~1, strata = ~ststr, weights = ~mmsawt, data = brfss2020)
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       -1.82683    0.02165 -84.367  < 2e-16 ***
## sexMale           -0.14290    0.03177  -4.498 6.87e-06 ***
## hlthpln1nohp       0.32917    0.05130   6.416 1.40e-10 ***
## checkup11last5yrs -0.28925    0.06287  -4.601 4.21e-06 ***
## checkup12never     0.09695    0.18888   0.513    0.608    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 0.9988613)
## 
## Number of Fisher Scoring iterations: 4

Based on the logistic regression, those who report having health coverage are less likely to report poor health compared to those who report not having health coverage with a statistical significance.

Interestingly enough, Those who report having a check up in the last 5 years are less likely to report poor health than those who have had a check up in the last year.This interesting finding is also statistically significant which is the opposite of what I though I was going to find.

Those who have never had a check up are more likely to report poor health compared to those who have had a check up in the last year, however, this is not statistically significant.

Present results from a model with sample weights and design effects, if your data allow for this. Present the results in tabular form, with Parameter estimates, odds ratios (if using the logit model) and confidence intervals for the odds ratios.

library(gtsummary)
fit.logit%>%
  tbl_regression(exponentiate=TRUE )

Characteristic	OR1	95% CI1	p-value
sex
Female	—	—
Male	0.87	0.81, 0.92	<0.001
HAVE ANY HEALTH CARE COVERAGE
hp	—	—
nohp	1.39	1.26, 1.54	<0.001
checkup1
0last2yrs	—	—
1last5yrs	0.75	0.66, 0.85	<0.001
2never	1.10	0.76, 1.60	0.6
1 OR = Odds Ratio, CI = Confidence Interval

Men are 13% less likely, compared to women, to report bad health.

Those who do not have a health plan are 39% more likely, compared to those who have a health plan, to report bad health.

Those who reported having a check up within the last 5 years are 25% less likely, compared tot hose who reported having a check up within the last year, to report poor health.

Generate predicted probabilities for some “interesting” cases from your analysis, to highlight the effects from the model and your stated research question.

The specific cases I am interested are women who have health coverage but have had a check up within the last 5 years and women who do not have health coverage but have had a check up more recently, within the last year. I chose these cases because I am curious to see if having a recent check up can off set not having a health plan or vice versa.

comps<-as.data.frame(marg_logit)

comps[comps$hlthpln1=="hp" & comps$checkup1 == "1last5yrs" , ]

comps[comps$hlthpln1=="nohp" & comps$checkup1 == "0last2yrs" ,  ]

Based on the generated probabilities, a woman is more likely to report bad health if she does not have health coverage even though she had a check up within the last year compared to a woman whose last check up was sometime within the last 5 years but has a health plan. This can support the idea that those that have a health plan feel they are healthier than those who have annual check ups.