Homework 4
Ron Neimark
2024-06-10
- Perform an appropriate hypothesis test to determine whether there is a statistical difference in mean sleep duration between those who are MetS+ and those who are MetS-. What can you conclude about the association between sleep duration and MetS? (5 points)
mets_sleep %>%
group_by(MetS) %>%
summarise(mean = mean(sleep, na.rm = T),
sd = sd(sleep, na.rm = T))| MetS | mean | sd |
|---|---|---|
| MetS+ | 7.42 | 1.53 |
| MetS- | 7.44 | 1.46 |
density <- mets_sleep %>%
filter(!is.na(sleep)) %>%
group_by(MetS) %>%
mutate(m = mean(sleep, na.rm=T)) %>%
#ungroup %>%
ggplot(aes(x=sleep)) +
geom_density(aes(fill=MetS, linetype=MetS),
color="darkgray",
linewidth=.5,
alpha=.2) +
geom_vline(aes(xintercept = m, color=MetS), linetype=2, size=.5) +
xlab("Hours of Sleep") +
ylab(NULL)## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.density
The distribution is not normal (left-skewed).
density +
scale_x_continuous(trans = "log")
Log transformation makes the distribution even more skewed.
The SD and mean are pretty close. I would guess that the variances are equal, but I will run the Levene Test to verify.
# Perform levene test to determine whether variance of the distributions are the same.
variance = leveneTest(sleep ~ MetS, mets_sleep)
print(variance)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 3.7178 0.05395 .
## 2417
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1p-value of the levene test of homogeneity = 0.054, which is >0.05. Hence, the variance of the two groups is equal.
#perform t-test with equal variances
mets_sleep %>%
mutate(MetS = relevel(MetS, ref="MetS-")) %>%
ungroup() %>%
t_test(sleep ~ MetS, detailed=TRUE, var.equal=T)| estimate | estimate1 | estimate2 | .y. | group1 | group2 | n1 | n2 | statistic | p | df | conf.low | conf.high | method | alternative |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.0213 | 7.44 | 7.42 | sleep | MetS- | MetS+ | 1514 | 905 | 0.341 | 0.733 | 2.42e+03 | -0.101 | 0.144 | T-test | two.sided |
***We are unable to reject the null hypothesis, and it appears that the mean of sleep duration is the same in both the MetS+ and MetS- groups.
Since the assumption of normality of the distribution is violated, I will also run the Mann-Whitney test.**
wilcox.test(sleep ~ MetS, data = mets_sleep)##
## Wilcoxon rank sum test with continuity correction
##
## data: sleep by MetS
## W = 684585, p-value = 0.9758
## alternative hypothesis: true location shift is not equal to 0Again, we cannot reject the null and we are fairly confident that the difference of the means is 0, and that the average sleep duration of those presenting with evidence of Metabolic Syndrome is no different from the average sleep duration of those who do not present with it.
- Estimate the odds ratio of the association between MetS and sex, and compute the 95% confidence interval. Briefly state your conclusions. (5 points)
mets_sleep %>%
mutate(MetS = relevel(MetS, ref="MetS-"),
sex = relevel(sex, ref="Male"),
race = relevel(race, ref="White")) %>%
contingency(MetS ~ sex)## Outcome
## Predictor MetS+ MetS-
## Female 501 739
## Male 404 775
##
## Outcome + Outcome - Total Inc risk *
## Exposed + 501 739 1240 40.40 (37.66 to 43.19)
## Exposed - 404 775 1179 34.27 (31.56 to 37.05)
## Total 905 1514 2419 37.41 (35.48 to 39.38)
##
## Point estimates and 95% CIs:
## -------------------------------------------------------------------
## Inc risk ratio 1.18 (1.06, 1.31)
## Inc odds ratio 1.30 (1.10, 1.53)
## Attrib risk in the exposed * 6.14 (2.29, 9.98)
## Attrib fraction in the exposed (%) 15.19 (5.89, 23.57)
## Attrib risk in the population * 3.15 (-0.18, 6.47)
## Attrib fraction in the population (%) 8.41 (2.97, 13.54)
## -------------------------------------------------------------------
## Uncorrected chi2 test that OR = 1: chi2(1) = 9.721 Pr>chi2 = 0.002
## Fisher exact test that OR = 1: Pr>chi2 = 0.002
## Wald confidence limits
## CI: confidence interval
## * Outcomes per 100 population units
##
##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: dat
## X-squared = 9.4603, df = 1, p-value = 0.0021Females have a 30% greater odds of being MetS+ than males (OR=1.30, 95% CI = 1.10, 1.53).
- Test whether there is an association between MetS and sex using a chi-squared test of independence. State your conclusions and describe whether they match the conclusions in the previous question. (5 points)
As also revealed in the outcome of the contingency procedure run in the previous question…. The results remain the same.
chisq.test(mets_sleep$MetS, mets_sleep$sex)##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: mets_sleep$MetS and mets_sleep$sex
## X-squared = 9.4603, df = 1, p-value = 0.0021- Perform logistic regression to model the relationship between MetS and sleep duration where (i) sleep duration is treated as categorical and (ii) sleep duration is treated as numeric. For categorical sleep duration, round the sleep variable to the nearest hour and convert to factor.
**First the logistic model with sleep as a continuous variable
logistic_model1 <- glm(MetS ~ sleep, family=binomial (link='logit'), data = regression_relevel)
anova(logistic_model1, test="Chisq")| Df | Deviance | Resid. Df | Resid. Dev | Pr(>Chi) |
|---|---|---|---|---|
| 2418 | 3.2e+03 | |||
| 1 | 0.116 | 2417 | 3.2e+03 | 0.733 |
summary(logistic_model1)##
## Call:
## glm(formula = MetS ~ sleep, family = binomial(link = "logit"),
## data = regression_relevel)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.443134 0.213692 -2.074 0.0381 *
## sleep -0.009612 0.028201 -0.341 0.7332
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 3198.5 on 2418 degrees of freedom
## Residual deviance: 3198.3 on 2417 degrees of freedom
## AIC: 3202.3
##
## Number of Fisher Scoring iterations: 4** Then with sleep as a Factor**
logistic_model2 <- glm(MetS ~ sleep_factor, family=binomial (link='logit'), data = regression_relevel)
anova(logistic_model2, test="Chisq")| Df | Deviance | Resid. Df | Resid. Dev | Pr(>Chi) |
|---|---|---|---|---|
| 2418 | 3.2e+03 | |||
| 8 | 9.42 | 2410 | 3.19e+03 | 0.308 |
summary(logistic_model2)##
## Call:
## glm(formula = MetS ~ sleep_factor, family = binomial(link = "logit"),
## data = regression_relevel)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.62357 0.07097 -8.787 <2e-16 ***
## sleep_factor2 0.06395 0.63079 0.101 0.9192
## sleep_factor3 0.40043 0.47962 0.835 0.4038
## sleep_factor4 0.41226 0.24137 1.708 0.0876 .
## sleep_factor5 0.23410 0.21207 1.104 0.2696
## sleep_factor6 0.11754 0.12097 0.972 0.3312
## sleep_factor7 0.04908 0.12636 0.388 0.6977
## sleep_factor9 0.35391 0.13796 2.565 0.0103 *
## sleep_factor10 0.10227 0.16127 0.634 0.5260
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 3198.5 on 2418 degrees of freedom
## Residual deviance: 3189.0 on 2410 degrees of freedom
## AIC: 3207
##
## Number of Fisher Scoring iterations: 4- Tabulate the estimated ORs, p-values, and 95% Cis, and present your results in a single table. (5 points)
tab_or <- tab_model(logistic_model1, logistic_model2)tab_or| Met S | Met S | |||||
|---|---|---|---|---|---|---|
| Predictors | Odds Ratios | CI | p | Odds Ratios | CI | p |
| (Intercept) | 0.64 | 0.42 – 0.97 | 0.038 | 0.54 | 0.47 – 0.62 | <0.001 |
|
Sleep hours-weekdays or workdays |
0.99 | 0.94 – 1.05 | 0.733 | |||
|
sleep factor: Sleep hours-weekdays or workdays: sleep factor 2 |
1.07 | 0.28 – 3.56 | 0.919 | |||
|
sleep factor: Sleep hours-weekdays or workdays: sleep factor 3 |
1.49 | 0.56 – 3.82 | 0.404 | |||
|
sleep factor: Sleep hours-weekdays or workdays: sleep factor 4 |
1.51 | 0.94 – 2.42 | 0.088 | |||
|
sleep factor: Sleep hours-weekdays or workdays: sleep factor 5 |
1.26 | 0.83 – 1.91 | 0.270 | |||
|
sleep factor: Sleep hours-weekdays or workdays: sleep factor 6 |
1.12 | 0.89 – 1.42 | 0.331 | |||
|
sleep factor: Sleep hours-weekdays or workdays: sleep factor 7 |
1.05 | 0.82 – 1.34 | 0.698 | |||
|
sleep factor: Sleep hours-weekdays or workdays: sleep factor 9 |
1.42 | 1.09 – 1.87 | 0.010 | |||
|
sleep factor: Sleep hours-weekdays or workdays: sleep factor 10 |
1.11 | 0.81 – 1.52 | 0.526 | |||
| Observations | 2419 | 2419 | ||||
| R2 Tjur | 0.000 | 0.004 | ||||
- Compute the predicted proportion of MetS+ for the different hours of sleep duration based on each model above. Plot these estimated values as points and add error bars to denote the 95% CI. Plot each model values separately. Improve the appearance of the plots. (5 points)
glm_plot1 <- plot_model(logistic_model1, type="pred")
glm_plot1
glm_plot2 <- plot_model(logistic_model2, type="pred")
glm_plot2
- Bonus: Plot both model-predicted values and error bars in a single figure, using different colors for each model. (5 points)
- Repeat the above logistic models, adjusting for the variables in Table 2 of Smiley et al. (not including Sitting). Tabulate the estimated odds ratios, p-values, and 95% CI. Display the results of all four models in a single table. Comment on whether the model covariates are potential confounders. (5 points)
logistic_model3 <- glm(MetS ~ sleep_factor + age_scale, family=binomial (link='logit'), data = regression_relevel)
logistic_model4 <- glm(MetS ~ sleep + age_scale, family=binomial (link='logit'), data = regression_relevel)
logistic_model5 <- glm(MetS ~ sleep_factor + sex, family=binomial (link='logit'), data = regression_relevel)
logistic_model6 <- glm(MetS ~ sleep + sex, family=binomial (link='logit'), data = regression_relevel)tab_or2 <- tab_model(logistic_model3,
logistic_model4,
logistic_model5,
logistic_model6)
tab_or2| Met S | Met S | Met S | Met S | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Predictors | Odds Ratios | CI | p | Odds Ratios | CI | p | Odds Ratios | CI | p | Odds Ratios | CI | p |
| (Intercept) | 0.23 | 0.19 – 0.29 | <0.001 | 0.32 | 0.21 – 0.50 | <0.001 | 0.46 | 0.39 – 0.54 | <0.001 | 0.58 | 0.38 – 0.89 | 0.012 |
|
Sleep hours-weekdays or workdays: sleep factor: sleep factor 2 |
1.06 | 0.27 – 3.64 | 0.922 | 1.02 | 0.26 – 3.40 | 0.980 | ||||||
|
Sleep hours-weekdays or workdays: sleep factor: sleep factor 3 |
1.48 | 0.55 – 3.88 | 0.424 | 1.45 | 0.55 – 3.72 | 0.441 | ||||||
|
Sleep hours-weekdays or workdays: sleep factor: sleep factor 4 |
1.52 | 0.93 – 2.46 | 0.091 | 1.53 | 0.95 – 2.46 | 0.078 | ||||||
|
Sleep hours-weekdays or workdays: sleep factor: sleep factor 5 |
1.24 | 0.81 – 1.90 | 0.314 | 1.32 | 0.86 – 2.00 | 0.194 | ||||||
|
Sleep hours-weekdays or workdays: sleep factor: sleep factor 6 |
1.13 | 0.89 – 1.44 | 0.306 | 1.15 | 0.91 – 1.46 | 0.242 | ||||||
|
Sleep hours-weekdays or workdays: sleep factor: sleep factor 7 |
1.04 | 0.81 – 1.34 | 0.735 | 1.07 | 0.83 – 1.37 | 0.587 | ||||||
|
Sleep hours-weekdays or workdays: sleep factor: sleep factor 9 |
1.34 | 1.01 – 1.77 | 0.040 | 1.43 | 1.09 – 1.88 | 0.009 | ||||||
|
Sleep hours-weekdays or workdays: sleep factor: sleep factor 10 |
0.94 | 0.68 – 1.30 | 0.707 | 1.10 | 0.80 – 1.51 | 0.537 | ||||||
| Age in years at screening | 1.03 | 1.02 – 1.03 | <0.001 | 1.03 | 1.02 – 1.03 | <0.001 | ||||||
|
Sleep hours-weekdays or workdays |
0.97 | 0.92 – 1.03 | 0.271 | 0.99 | 0.93 – 1.04 | 0.598 | ||||||
| sex: Female | 1.31 | 1.11 – 1.55 | 0.001 | 1.30 | 1.11 – 1.54 | 0.002 | ||||||
| Observations | 2419 | 2419 | 2419 | 2419 | ||||||||
| R2 Tjur | 0.048 | 0.045 | 0.008 | 0.004 | ||||||||
None of the co-variates were greater than 10% different from the covariates in the crude model. It is unlikely that any of the covariates are confounders.
- Use linear regression to assess the relationship between Systolic Blood Pressure (SBP) and sleep duration (numeric), adjusting for the demographic variables in Table 1 (sex, ethnicity, marital status, education) and fasting glucose.
summary(lm(sleep~sys_scale, data=regression_relevel))##
## Call:
## lm(formula = sleep ~ sys_scale, data = regression_relevel)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.4470 -0.9315 0.0666 1.0573 3.0900
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.43489 0.03028 245.564 <2e-16 ***
## sys_scale -0.01291 0.03028 -0.426 0.67
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.489 on 2417 degrees of freedom
## Multiple R-squared: 7.518e-05, Adjusted R-squared: -0.0003385
## F-statistic: 0.1817 on 1 and 2417 DF, p-value: 0.6699model0 <- lm(sleep ~ sys_scale, data = regression_relevel)
anova(model0)| Df | Sum Sq | Mean Sq | F value | Pr(>F) |
|---|---|---|---|---|
| 1 | 0.403 | 0.403 | 0.182 | 0.67 |
| 2417 | 5.36e+03 | 2.22 |
summary(model0)##
## Call:
## lm(formula = sleep ~ sys_scale, data = regression_relevel)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.4470 -0.9315 0.0666 1.0573 3.0900
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.43489 0.03028 245.564 <2e-16 ***
## sys_scale -0.01291 0.03028 -0.426 0.67
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.489 on 2417 degrees of freedom
## Multiple R-squared: 7.518e-05, Adjusted R-squared: -0.0003385
## F-statistic: 0.1817 on 1 and 2417 DF, p-value: 0.6699model1 <- lm(sleep ~ sys_scale + sex + race + marital + education + glucose_scale, data = regression_relevel)
anova(model1)| Df | Sum Sq | Mean Sq | F value | Pr(>F) |
|---|---|---|---|---|
| 1 | 0.403 | 0.403 | 0.185 | 0.667 |
| 1 | 18.8 | 18.8 | 8.62 | 0.00335 |
| 4 | 77.3 | 19.3 | 8.89 | 4.04e-07 |
| 3 | 23.5 | 7.83 | 3.6 | 0.013 |
| 4 | 9.4 | 2.35 | 1.08 | 0.365 |
| 1 | 1.98 | 1.98 | 0.911 | 0.34 |
| 2403 | 5.23e+03 | 2.18 |
summary(model1)##
## Call:
## lm(formula = sleep ~ sys_scale + sex + race + marital + education +
## glucose_scale, data = regression_relevel)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.5920 -0.8512 0.0532 0.9757 3.4725
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.633859 0.126799 60.205 < 2e-16 ***
## sys_scale -0.001734 0.031629 -0.055 0.95628
## sexFemale 0.148365 0.061324 2.419 0.01562 *
## raceHispanic -0.162037 0.088011 -1.841 0.06573 .
## raceBlack -0.463822 0.083033 -5.586 2.59e-08 ***
## raceAsian -0.017238 0.099171 -0.174 0.86202
## raceMultiracial (Other) -0.161546 0.139862 -1.155 0.24819
## maritalMarried or Living with partner -0.022851 0.084023 -0.272 0.78567
## maritalWidowed 0.386489 0.137287 2.815 0.00491 **
## maritalDivorced or Separated -0.002916 0.105602 -0.028 0.97798
## education< 9th grade -0.226687 0.140144 -1.618 0.10589
## educationHigh School -0.186037 0.107109 -1.737 0.08254 .
## educationSome College -0.141982 0.102905 -1.380 0.16780
## education>= College Graduate -0.094366 0.110710 -0.852 0.39409
## glucose_scale -0.029337 0.030743 -0.954 0.34005
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.475 on 2403 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.02451, Adjusted R-squared: 0.01883
## F-statistic: 4.313 on 14 and 2403 DF, p-value: 1.282e-07Sex, Race and Marital Status are all significant and could have an effect on the relationship between sBP and sleep duration. I will run a model testing effect modification of those particular covariates.
model2 <- lm(sleep ~ sys_scale + sex + race + marital + race*sys_scale + sex*sys_scale + marital*sys_scale, data = regression_relevel)
anova(model2)| Df | Sum Sq | Mean Sq | F value | Pr(>F) |
|---|---|---|---|---|
| 1 | 0.403 | 0.403 | 0.186 | 0.667 |
| 1 | 18.7 | 18.7 | 8.59 | 0.0034 |
| 4 | 76.9 | 19.2 | 8.85 | 4.29e-07 |
| 3 | 23.5 | 7.83 | 3.61 | 0.0129 |
| 4 | 5.32 | 1.33 | 0.613 | 0.654 |
| 1 | 0.329 | 0.329 | 0.152 | 0.697 |
| 3 | 23.4 | 7.8 | 3.59 | 0.0131 |
| 2401 | 5.21e+03 | 2.17 |
summary(model2)##
## Call:
## lm(formula = sleep ~ sys_scale + sex + race + marital + race *
## sys_scale + sex * sys_scale + marital * sys_scale, data = regression_relevel)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.6689 -0.8079 0.0553 0.9905 3.4221
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 7.46898 0.09412 79.355
## sys_scale -0.16465 0.10205 -1.613
## sexFemale 0.14890 0.06114 2.435
## raceHispanic -0.17711 0.08196 -2.161
## raceBlack -0.46967 0.08345 -5.628
## raceAsian -0.02056 0.09612 -0.214
## raceMultiracial (Other) -0.18053 0.14040 -1.286
## maritalMarried or Living with partner 0.01413 0.08515 0.166
## maritalWidowed 0.27108 0.15007 1.806
## maritalDivorced or Separated 0.02356 0.10615 0.222
## sys_scale:raceHispanic -0.02799 0.08808 -0.318
## sys_scale:raceBlack 0.04121 0.08138 0.506
## sys_scale:raceAsian -0.08797 0.10026 -0.877
## sys_scale:raceMultiracial (Other) -0.14408 0.14266 -1.010
## sys_scale:sexFemale -0.02630 0.06277 -0.419
## sys_scale:maritalMarried or Living with partner 0.20708 0.08631 2.399
## sys_scale:maritalWidowed 0.38889 0.12584 3.090
## sys_scale:maritalDivorced or Separated 0.21374 0.10513 2.033
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## sys_scale 0.10677
## sexFemale 0.01495 *
## raceHispanic 0.03079 *
## raceBlack 2.03e-08 ***
## raceAsian 0.83063
## raceMultiracial (Other) 0.19862
## maritalMarried or Living with partner 0.86825
## maritalWidowed 0.07099 .
## maritalDivorced or Separated 0.82440
## sys_scale:raceHispanic 0.75071
## sys_scale:raceBlack 0.61266
## sys_scale:raceAsian 0.38038
## sys_scale:raceMultiracial (Other) 0.31260
## sys_scale:sexFemale 0.67528
## sys_scale:maritalMarried or Living with partner 0.01650 *
## sys_scale:maritalWidowed 0.00202 **
## sys_scale:maritalDivorced or Separated 0.04216 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.473 on 2401 degrees of freedom
## Multiple R-squared: 0.02769, Adjusted R-squared: 0.02081
## F-statistic: 4.023 on 17 and 2401 DF, p-value: 5.467e-08Marital status appears to have significant effects modification on the relationship between systolic blood pressure and sleep duration. Age and race do not.
model3 <- lm(sleep ~ sys_scale + sex + race + marital + education + glucose_scale + marital*sys_scale, data = regression_relevel)
anova(model3)| Df | Sum Sq | Mean Sq | F value | Pr(>F) |
|---|---|---|---|---|
| 1 | 0.403 | 0.403 | 0.186 | 0.667 |
| 1 | 18.8 | 18.8 | 8.65 | 0.0033 |
| 4 | 77.3 | 19.3 | 8.91 | 3.85e-07 |
| 3 | 23.5 | 7.83 | 3.61 | 0.0128 |
| 4 | 9.4 | 2.35 | 1.08 | 0.363 |
| 1 | 1.98 | 1.98 | 0.913 | 0.339 |
| 3 | 21.9 | 7.3 | 3.37 | 0.0179 |
| 2400 | 5.21e+03 | 2.17 |
summary(model3)##
## Call:
## lm(formula = sleep ~ sys_scale + sex + race + marital + education +
## glucose_scale + marital * sys_scale, data = regression_relevel)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.6175 -0.8189 0.0717 0.9720 3.4571
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 7.59503 0.12781 59.426
## sys_scale -0.17611 0.07211 -2.442
## sexFemale 0.15192 0.06131 2.478
## raceHispanic -0.15996 0.08801 -1.818
## raceBlack -0.46366 0.08310 -5.579
## raceAsian -0.03034 0.09918 -0.306
## raceMultiracial (Other) -0.16614 0.13969 -1.189
## maritalMarried or Living with partner 0.01893 0.08547 0.222
## maritalWidowed 0.28872 0.15169 1.903
## maritalDivorced or Separated 0.03087 0.10668 0.289
## education< 9th grade -0.22784 0.13997 -1.628
## educationHigh School -0.18765 0.10702 -1.753
## educationSome College -0.14254 0.10279 -1.387
## education>= College Graduate -0.09883 0.11063 -0.893
## glucose_scale -0.02587 0.03077 -0.841
## sys_scale:maritalMarried or Living with partner 0.18730 0.08282 2.262
## sys_scale:maritalWidowed 0.37493 0.12444 3.013
## sys_scale:maritalDivorced or Separated 0.20909 0.10454 2.000
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## sys_scale 0.01467 *
## sexFemale 0.01329 *
## raceHispanic 0.06925 .
## raceBlack 2.69e-08 ***
## raceAsian 0.75969
## raceMultiracial (Other) 0.23442
## maritalMarried or Living with partner 0.82472
## maritalWidowed 0.05712 .
## maritalDivorced or Separated 0.77230
## education< 9th grade 0.10371
## educationHigh School 0.07966 .
## educationSome College 0.16567
## education>= College Graduate 0.37174
## glucose_scale 0.40049
## sys_scale:maritalMarried or Living with partner 0.02381 *
## sys_scale:maritalWidowed 0.00261 **
## sys_scale:maritalDivorced or Separated 0.04561 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.473 on 2400 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.0286, Adjusted R-squared: 0.02172
## F-statistic: 4.156 on 17 and 2400 DF, p-value: 2.29e-08- Assess the model assumption of normality of residuals using appropriate plots. What can you conclude? (5 points)
ggplot() +
geom_qq(aes(sample = rstandard(model3))) +
geom_abline(color = "red") +
coord_fixed()+
ggtitle("Q-Q Residuals")+
labs(x="Standardized Residuals",
y="Theoretical Quantiles")
The assumption of normality is violated.
- Tabulate model estimates, confidence intervals, and p-values. Briefly describe the adjusted relationship between SBP and sleep duration and comment on its statistical significance. (5 points)
tab_model(model0, model1, model2, model3)|
Sleep hours-weekdays or workdays |
Sleep hours-weekdays or workdays |
Sleep hours-weekdays or workdays |
Sleep hours-weekdays or workdays |
|||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Predictors | Estimates | CI | p | Estimates | CI | p | Estimates | CI | p | Estimates | CI | p |
| (Intercept) | 7.43 | 7.38 – 7.49 | <0.001 | 7.63 | 7.39 – 7.88 | <0.001 | 7.47 | 7.28 – 7.65 | <0.001 | 7.60 | 7.34 – 7.85 | <0.001 |
| sys scale | -0.01 | -0.07 – 0.05 | 0.670 | -0.00 | -0.06 – 0.06 | 0.956 | -0.16 | -0.36 – 0.04 | 0.107 | -0.18 | -0.32 – -0.03 | 0.015 |
| sex [Female] | 0.15 | 0.03 – 0.27 | 0.016 | 0.15 | 0.03 – 0.27 | 0.015 | 0.15 | 0.03 – 0.27 | 0.013 | |||
| race [Hispanic] | -0.16 | -0.33 – 0.01 | 0.066 | -0.18 | -0.34 – -0.02 | 0.031 | -0.16 | -0.33 – 0.01 | 0.069 | |||
| race [Black] | -0.46 | -0.63 – -0.30 | <0.001 | -0.47 | -0.63 – -0.31 | <0.001 | -0.46 | -0.63 – -0.30 | <0.001 | |||
| race [Asian] | -0.02 | -0.21 – 0.18 | 0.862 | -0.02 | -0.21 – 0.17 | 0.831 | -0.03 | -0.22 – 0.16 | 0.760 | |||
|
race [Multiracial (Other)] |
-0.16 | -0.44 – 0.11 | 0.248 | -0.18 | -0.46 – 0.09 | 0.199 | -0.17 | -0.44 – 0.11 | 0.234 | |||
|
marital [Married or Living with partner] |
-0.02 | -0.19 – 0.14 | 0.786 | 0.01 | -0.15 – 0.18 | 0.868 | 0.02 | -0.15 – 0.19 | 0.825 | |||
| marital [Widowed] | 0.39 | 0.12 – 0.66 | 0.005 | 0.27 | -0.02 – 0.57 | 0.071 | 0.29 | -0.01 – 0.59 | 0.057 | |||
|
marital [Divorced or Separated] |
-0.00 | -0.21 – 0.20 | 0.978 | 0.02 | -0.18 – 0.23 | 0.824 | 0.03 | -0.18 – 0.24 | 0.772 | |||
| education [< 9th grade] | -0.23 | -0.50 – 0.05 | 0.106 | -0.23 | -0.50 – 0.05 | 0.104 | ||||||
| education [High School] | -0.19 | -0.40 – 0.02 | 0.083 | -0.19 | -0.40 – 0.02 | 0.080 | ||||||
| education [Some College] | -0.14 | -0.34 – 0.06 | 0.168 | -0.14 | -0.34 – 0.06 | 0.166 | ||||||
|
education [>= College Graduate] |
-0.09 | -0.31 – 0.12 | 0.394 | -0.10 | -0.32 – 0.12 | 0.372 | ||||||
| glucose scale | -0.03 | -0.09 – 0.03 | 0.340 | -0.03 | -0.09 – 0.03 | 0.400 | ||||||
|
sys scale × race [Hispanic] |
-0.03 | -0.20 – 0.14 | 0.751 | |||||||||
| sys scale × race [Black] | 0.04 | -0.12 – 0.20 | 0.613 | |||||||||
| sys scale × race [Asian] | -0.09 | -0.28 – 0.11 | 0.380 | |||||||||
|
sys scale × race [Multiracial (Other)] |
-0.14 | -0.42 – 0.14 | 0.313 | |||||||||
| sys scale × sex [Female] | -0.03 | -0.15 – 0.10 | 0.675 | |||||||||
|
sys scale × marital [Married or Living with partner] |
0.21 | 0.04 – 0.38 | 0.016 | 0.19 | 0.02 – 0.35 | 0.024 | ||||||
|
sys scale × marital [Widowed] |
0.39 | 0.14 – 0.64 | 0.002 | 0.37 | 0.13 – 0.62 | 0.003 | ||||||
|
sys scale × marital [Divorced or Separated] |
0.21 | 0.01 – 0.42 | 0.042 | 0.21 | 0.00 – 0.41 | 0.046 | ||||||
| Observations | 2419 | 2418 | 2419 | 2418 | ||||||||
| R2 / R2 adjusted | 0.000 / -0.000 | 0.025 / 0.019 | 0.028 / 0.021 | 0.029 / 0.022 | ||||||||
When the model is adjusted for the effects modification of marital status on systolic blood pressure, systolic blood pressure becomes a significant predictor of sleep duration.