CCHS: Regression
This tutorial is for a complex data analysis, specifically using regression techniques to analyze survey data.
Let us load necessary R packages for the analysis:
Load data
Loads a dataset and provides some quick data checks, like the dimensions and summary of weights.
Logistic for complex survey
Performs a simple logistic regression using the complex survey data, focusing on the relationship between cardiovascular disease and osteoarthritis.
Multivariable analysis
Runs a more complex logistic regression model, adding multiple covariates to better understand the relationship.
formula1 <- as.formula(I(CVD=="event") ~ OA + age + sex + married + race +
edu + income + bmi + phyact + doctor + stress +
smoke + drink + fruit + bp + diab + province + immigrate)
fit3 <- svyglm(formula1,
design = w.design,
family = binomial(logit))
publish(fit3)
#> Variable Units OddsRatio CI.95 p-value
#> OA Control Ref
#> OA 1.52 [1.40;1.66] < 1e-04
#> age 20-29 years Ref
#> 30-39 years 1.29 [0.98;1.69] 0.0707636
#> 40-49 years 2.74 [2.17;3.47] < 1e-04
#> 50-59 years 6.24 [4.97;7.83] < 1e-04
#> 60-64 years 9.71 [7.68;12.29] < 1e-04
#> 65 years and over 15.85 [12.57;20.00] < 1e-04
#> teen 0.46 [0.20;1.07] 0.0707295
#> sex Female Ref
#> Male 1.73 [1.60;1.88] < 1e-04
#> married not single Ref
#> single 0.97 [0.90;1.05] 0.5209444
#> race Non-white Ref
#> White 1.44 [1.19;1.75] 0.0002219
#> edu < 2ndary Ref
#> 2nd grad. 0.90 [0.80;1.00] 0.0512330
#> Other 2nd grad. 0.97 [0.83;1.13] 0.6737665
#> Post-2nd grad. 0.93 [0.85;1.02] 0.1016562
#> income $29,999 or less Ref
#> $30,000-$49,999 0.74 [0.67;0.81] < 1e-04
#> $50,000-$79,999 0.64 [0.58;0.72] < 1e-04
#> $80,000 or more 0.58 [0.51;0.66] < 1e-04
#> bmi Underweight Ref
#> healthy weight 0.86 [0.67;1.10] 0.2350526
#> Overweight 0.88 [0.69;1.12] 0.3033213
#> phyact Active Ref
#> Inactive 1.21 [1.10;1.34] 0.0001345
#> Moderate 1.08 [0.97;1.21] 0.1771985
#> doctor No Ref
#> Yes 1.75 [1.49;2.06] < 1e-04
#> stress Not too stressed Ref
#> stressed 1.30 [1.18;1.42] < 1e-04
#> smoke Never smoker Ref
#> Current smoker 1.18 [1.05;1.32] 0.0050518
#> Former smoker 1.21 [1.11;1.33] < 1e-04
#> drink Never drank Ref
#> Current drinker 0.82 [0.68;0.98] 0.0290605
#> Former driker 1.13 [0.93;1.36] 0.2133779
#> fruit 0-3 daily serving Ref
#> 4-6 daily serving 0.94 [0.86;1.03] 0.1758214
#> 6+ daily serving 1.09 [0.97;1.23] 0.1311029
#> bp No Ref
#> Yes 2.35 [2.16;2.55] < 1e-04
#> diab No Ref
#> Yes 1.86 [1.66;2.07] < 1e-04
#> province South Ref
#> North 1.21 [0.90;1.62] 0.2103030
#> immigrate not immigrant Ref
#> > 10 years 1.02 [0.89;1.16] 0.8057243
#> recent 1.06 [0.73;1.53] 0.7651069Model fit assessment
Variability explained
Pseudo-R-square values indicate how much of the total variability in the outcomes is explainable by the fitted model (analogous to R-square). For a continuous outcome, we can compute R-square, while R-square cannot be calculated when the outcome variable is categorical, nominal or ordinal. We use pseudo-R-squared measures when the dependent variable is not continuous but a likelihood function is used to fit a model. Popular Pseudo-R-square measures are:
- Cox/Snell (never reaches max 1)
- Nagelkerke R-square (scaled to max 1)
- The larger Cox & Snell estimate is the better the model.
- These Pseudo-R-square values should be interpreted with caution (if not ignored).
- They offer little confidence in interpreting the model fit.
- Survey weighted version of them are available.
- Not trivial to decide which statistic to use under complex surveys.
Evaluates the model fit using Akaike Information Criterion (AIC) and pseudo R-squared metrics.
fit3 <- svyglm(formula1,
design = w.design,
family = quasibinomial(logit)) # publish does not work
AIC(fit3)
#> eff.p AIC deltabar
#> 67.752064 45362.706032 2.053093
# AIC for survey weighted regressions
psrsq(fit3, method = "Cox-Snell")
#> [1] 0.06091896
psrsq(fit3, method = "Nagelkerke")
#> [1] 0.2307586
# Nagelkerke and Cox-Snell pseudo-rsquared statisticsBackward Elimination
- Model comparisons
- LRT-aprroximation
- Wald-based
Checking one by one
Checks the significance of each variable one by one and removes those that are not statistically significant.
round(sort(summary(fit3)$coef[,"Pr(>|t|)"]),2)
#> (Intercept) age65 years and over bpYes
#> 0.00 0.00 0.00
#> age60-64 years age50-59 years sexMale
#> 0.00 0.00 0.00
#> diabYes OAOA income$80,000 or more
#> 0.00 0.00 0.00
#> age40-49 years income$50,000-$79,999 doctorYes
#> 0.00 0.00 0.00
#> income$30,000-$49,999 stressstressed smokeFormer smoker
#> 0.00 0.00 0.00
#> phyactInactive raceWhite smokeCurrent smoker
#> 0.00 0.00 0.01
#> drinkCurrent drinker edu2nd grad. ageteen
#> 0.03 0.05 0.07
#> age30-39 years eduPost-2nd grad. fruit6+ daily serving
#> 0.07 0.10 0.13
#> fruit4-6 daily serving phyactModerate provinceNorth
#> 0.18 0.18 0.21
#> drinkFormer driker bmihealthy weight bmiOverweight
#> 0.21 0.24 0.30
#> marriedsingle eduOther 2nd grad. immigraterecent
#> 0.52 0.67 0.77
#> immigrate> 10 years
#> 0.81
# bmiOverweight is associated with largest p-value
# but what about other categories?
regTermTest(fit3,~bmi) # coef of all bmi cat = 0
#> Wald test for bmi
#> in svyglm(formula = formula1, design = w.design, family = quasibinomial(logit))
#> F = 0.7591291 on 2 and 185579 df: p= 0.46808
fit4 <- update(fit3, .~. -bmi)
anova(fit3, fit4)
#> Working (Rao-Scott+F) LRT for bmi
#> in svyglm(formula = formula1, design = w.design, family = quasibinomial(logit))
#> Working 2logLR = 1.424634 p= 0.49071
#> (scale factors: 1.1 0.93 ); denominator df= 185579
# high p-value (in both wald and Anova) makes it more likely that you should exclude bmi
AIC(fit3,fit4)
#> eff.p AIC deltabar
#> [1,] 67.75206 45362.71 2.053093
#> [2,] 64.30460 45358.26 2.074342
round(sort(summary(fit4)$coef[,"Pr(>|t|)"]),2)
#> (Intercept) age65 years and over bpYes
#> 0.00 0.00 0.00
#> age60-64 years age50-59 years sexMale
#> 0.00 0.00 0.00
#> diabYes OAOA income$80,000 or more
#> 0.00 0.00 0.00
#> age40-49 years income$50,000-$79,999 doctorYes
#> 0.00 0.00 0.00
#> income$30,000-$49,999 stressstressed smokeFormer smoker
#> 0.00 0.00 0.00
#> phyactInactive raceWhite smokeCurrent smoker
#> 0.00 0.00 0.00
#> drinkCurrent drinker edu2nd grad. age30-39 years
#> 0.03 0.05 0.07
#> ageteen eduPost-2nd grad. fruit6+ daily serving
#> 0.07 0.10 0.13
#> fruit4-6 daily serving phyactModerate provinceNorth
#> 0.17 0.17 0.21
#> drinkFormer driker marriedsingle eduOther 2nd grad.
#> 0.21 0.53 0.67
#> immigraterecent immigrate> 10 years
#> 0.76 0.81Using AIC to automate
Uses stepwise regression guided by AIC to automatically select the most important variables.
require(MASS)
formula1b <- as.formula(I(CVD=="event") ~ OA + age + sex)
fit1b <- svyglm(formula1b,
design = w.design,
family = binomial(logit))
fit5 <- stepAIC(fit1b, direction = "backward")
#> Start: AIC=47384.51
#> I(CVD == "event") ~ OA + age + sex
#> Df Deviance AIC
#> <none> 47353 47385
#> - sex 1 47634 47658
#> - OA 1 47679 47702
#> - age 6 54414 54291publish(fit5)
#> Variable Units OddsRatio CI.95 p-value
#> OA Control Ref
#> OA 1.81 [1.66;1.97] < 1e-04
#> age 20-29 years Ref
#> 30-39 years 1.40 [1.07;1.84] 0.01374
#> 40-49 years 3.39 [2.69;4.27] < 1e-04
#> 50-59 years 9.42 [7.55;11.76] < 1e-04
#> 60-64 years 17.78 [14.22;22.23] < 1e-04
#> 65 years and over 33.82 [27.26;41.97] < 1e-04
#> teen 0.45 [0.20;1.02] 0.05462
#> sex Female Ref
#> Male 1.57 [1.46;1.69] < 1e-04
round(sort(summary(fit5)$coef[,"Pr(>|t|)"]),2)
#> (Intercept) age65 years and over age60-64 years
#> 0.00 0.00 0.00
#> age50-59 years OAOA sexMale
#> 0.00 0.00 0.00
#> age40-49 years age30-39 years ageteen
#> 0.00 0.01 0.05Using AIC, but keeping importants
Similar to the previous step but ensures certain important variables remain in the model.
formula1c <- as.formula(I(CVD=="event") ~ OA + age + sex + married + race +
edu + income + bmi + phyact + fruit + bp + diab +
doctor + stress + smoke + drink + province + immigrate)
scope <- list(upper = ~ OA + age + sex + married + race +
edu + income + bmi + phyact + fruit + bp + diab +
doctor + stress + smoke + drink + province + immigrate,
lower = ~ OA + age + sex + married + race +
edu + income + bmi + phyact + fruit + bp + diab)
fit1c <- svyglm(formula1c, design = w.design, family = binomial(logit))
fitstep <- step(fit1c, scope = scope, trace = FALSE, k = 2, direction = "backward")
# k = 2 gives the genuine AICpublish(fitstep)
#> Variable Units OddsRatio CI.95 p-value
#> OA Control Ref
#> OA 1.52 [1.40;1.66] < 1e-04
#> age 20-29 years Ref
#> 30-39 years 1.29 [0.98;1.70] 0.0697699
#> 40-49 years 2.74 [2.17;3.47] < 1e-04
#> 50-59 years 6.24 [4.97;7.83] < 1e-04
#> 60-64 years 9.71 [7.68;12.28] < 1e-04
#> 65 years and over 15.85 [12.57;19.98] < 1e-04
#> teen 0.46 [0.20;1.07] 0.0705660
#> sex Female Ref
#> Male 1.73 [1.60;1.88] < 1e-04
#> married not single Ref
#> single 0.97 [0.90;1.05] 0.5042496
#> race Non-white Ref
#> White 1.41 [1.18;1.70] 0.0001986
#> edu < 2ndary Ref
#> 2nd grad. 0.90 [0.80;1.00] 0.0524940
#> Other 2nd grad. 0.97 [0.83;1.13] 0.6732446
#> Post-2nd grad. 0.93 [0.85;1.02] 0.1045975
#> income $29,999 or less Ref
#> $30,000-$49,999 0.74 [0.67;0.81] < 1e-04
#> $50,000-$79,999 0.64 [0.58;0.72] < 1e-04
#> $80,000 or more 0.58 [0.51;0.66] < 1e-04
#> bmi Underweight Ref
#> healthy weight 0.86 [0.67;1.10] 0.2316915
#> Overweight 0.88 [0.69;1.12] 0.2982852
#> phyact Active Ref
#> Inactive 1.22 [1.10;1.34] 0.0001227
#> Moderate 1.08 [0.97;1.21] 0.1754422
#> fruit 0-3 daily serving Ref
#> 4-6 daily serving 0.94 [0.86;1.03] 0.1807666
#> 6+ daily serving 1.09 [0.97;1.23] 0.1295281
#> bp No Ref
#> Yes 2.35 [2.16;2.55] < 1e-04
#> diab No Ref
#> Yes 1.85 [1.66;2.07] < 1e-04
#> doctor No Ref
#> Yes 1.75 [1.49;2.05] < 1e-04
#> stress Not too stressed Ref
#> stressed 1.30 [1.18;1.42] < 1e-04
#> smoke Never smoker Ref
#> Current smoker 1.17 [1.05;1.31] 0.0053412
#> Former smoker 1.21 [1.10;1.33] < 1e-04
#> drink Never drank Ref
#> Current drinker 0.82 [0.68;0.98] 0.0254942
#> Former driker 1.12 [0.93;1.36] 0.2205315
round(sort(summary(fitstep)$coef[,"Pr(>|t|)"]),2)
#> (Intercept) age65 years and over bpYes
#> 0.00 0.00 0.00
#> age60-64 years age50-59 years sexMale
#> 0.00 0.00 0.00
#> diabYes OAOA income$80,000 or more
#> 0.00 0.00 0.00
#> age40-49 years income$50,000-$79,999 doctorYes
#> 0.00 0.00 0.00
#> income$30,000-$49,999 stressstressed smokeFormer smoker
#> 0.00 0.00 0.00
#> phyactInactive raceWhite smokeCurrent smoker
#> 0.00 0.00 0.01
#> drinkCurrent drinker edu2nd grad. age30-39 years
#> 0.03 0.05 0.07
#> ageteen eduPost-2nd grad. fruit6+ daily serving
#> 0.07 0.10 0.13
#> phyactModerate fruit4-6 daily serving drinkFormer driker
#> 0.18 0.18 0.22
#> bmihealthy weight bmiOverweight marriedsingle
#> 0.23 0.30 0.50
#> eduOther 2nd grad.
#> 0.67Assess interactions
Check biologically interesting ones.
Check one by one
Checks if there is a significant interaction effect between ‘age’ and ‘sex’.
fit8a <- update(fitstep, .~. + interaction(age,sex))
anova(fitstep, fit8a) # keep interaction
#> Working (Rao-Scott+F) LRT for interaction(age, sex)
#> in svyglm(formula = I(CVD == "event") ~ OA + age + sex + married +
#> race + edu + income + bmi + phyact + fruit + bp + diab +
#> doctor + stress + smoke + drink + interaction(age, sex),
#> design = w.design, family = binomial(logit))
#> Working 2logLR = 40.16528 p= 1.2167e-06
#> (scale factors: 1.3 1.2 1.2 0.93 0.78 0.71 ); denominator df= 185576Checks if there is a significant interaction effect between ‘sex’ and ‘diabetes’.
fit8b <- update(fitstep, .~. + interaction(sex,diab))
anova(fitstep, fit8b) # Do not keep this interaction
#> Working (Rao-Scott+F) LRT for interaction(sex, diab)
#> in svyglm(formula = I(CVD == "event") ~ OA + age + sex + married +
#> race + edu + income + bmi + phyact + fruit + bp + diab +
#> doctor + stress + smoke + drink + interaction(sex, diab),
#> design = w.design, family = binomial(logit))
#> Working 2logLR = 0.4591456 p= 0.49597
#> df=1; denominator df= 185581Checks if there is a significant interaction effect between ‘BMI’ and ‘diabetes’.
fit8c <- update(fitstep, .~. + interaction(bmi,diab))
anova(fitstep, fit8c) # keep this interaction
#> Working (Rao-Scott+F) LRT for interaction(bmi, diab)
#> in svyglm(formula = I(CVD == "event") ~ OA + age + sex + married +
#> race + edu + income + bmi + phyact + fruit + bp + diab +
#> doctor + stress + smoke + drink + interaction(bmi, diab),
#> design = w.design, family = binomial(logit))
#> Working 2logLR = 7.92727 p= 0.02533
#> (scale factors: 1.4 0.6 ); denominator df= 185580Add all significant interactions in 1 model
Updates the model to include significant interaction terms.
Note that we have 0 effect modifier, 2 interactions
fit9 <- update(fitstep, .~. + interaction(age,sex) + interaction(bmi,diab))
require(jtools)
summ(fit9, confint = TRUE, digits = 3)| Observations | 185613 |
| Dependent variable | I(CVD == "event") |
| Type | Survey-weighted generalized linear model |
| Family | binomial |
| Link | logit |
| Pseudo-R² (Cragg-Uhler) | 0.233 |
| Pseudo-R² (McFadden) | 0.207 |
| AIC | 41548.160 |
| Est. | 2.5% | 97.5% | t val. | p | |
|---|---|---|---|---|---|
| (Intercept) | -5.590 | -6.046 | -5.135 | -24.069 | 0.000 |
| OAOA | 0.438 | 0.352 | 0.523 | 10.043 | 0.000 |
| age30-39 years | 0.299 | -0.118 | 0.717 | 1.405 | 0.160 |
| age40-49 years | 1.158 | 0.794 | 1.522 | 6.236 | 0.000 |
| age50-59 years | 2.181 | 1.831 | 2.531 | 12.212 | 0.000 |
| age60-64 years | 2.619 | 2.263 | 2.976 | 14.395 | 0.000 |
| age65 years and over | 3.033 | 2.680 | 3.387 | 16.833 | 0.000 |
| ageteen | -0.695 | -1.704 | 0.314 | -1.350 | 0.177 |
| sexMale | -0.028 | -0.447 | 0.390 | -0.133 | 0.895 |
| marriedsingle | -0.016 | -0.096 | 0.064 | -0.382 | 0.703 |
| raceWhite | 0.348 | 0.165 | 0.531 | 3.724 | 0.000 |
| edu2nd grad. | -0.107 | -0.217 | 0.003 | -1.906 | 0.057 |
| eduOther 2nd grad. | -0.039 | -0.192 | 0.114 | -0.498 | 0.618 |
| eduPost-2nd grad. | -0.081 | -0.173 | 0.010 | -1.746 | 0.081 |
| income$30,000-$49,999 | -0.304 | -0.400 | -0.208 | -6.215 | 0.000 |
| income$50,000-$79,999 | -0.444 | -0.552 | -0.336 | -8.034 | 0.000 |
| income$80,000 or more | -0.555 | -0.684 | -0.426 | -8.424 | 0.000 |
| bmihealthy weight | -1.406 | -2.677 | -0.135 | -2.167 | 0.030 |
| bmiOverweight | -1.110 | -2.375 | 0.154 | -1.721 | 0.085 |
| phyactInactive | 0.194 | 0.094 | 0.293 | 3.817 | 0.000 |
| phyactModerate | 0.077 | -0.034 | 0.187 | 1.353 | 0.176 |
| fruit4-6 daily serving | -0.062 | -0.155 | 0.031 | -1.313 | 0.189 |
| fruit6+ daily serving | 0.094 | -0.023 | 0.211 | 1.579 | 0.114 |
| bpYes | 0.861 | 0.778 | 0.944 | 20.354 | 0.000 |
| diabYes | 1.745 | 0.462 | 3.027 | 2.667 | 0.008 |
| doctorYes | 0.535 | 0.372 | 0.697 | 6.447 | 0.000 |
| stressstressed | 0.256 | 0.164 | 0.347 | 5.483 | 0.000 |
| smokeCurrent smoker | 0.152 | 0.039 | 0.266 | 2.628 | 0.009 |
| smokeFormer smoker | 0.177 | 0.082 | 0.272 | 3.654 | 0.000 |
| drinkCurrent drinker | -0.205 | -0.381 | -0.029 | -2.277 | 0.023 |
| drinkFormer driker | 0.116 | -0.072 | 0.303 | 1.210 | 0.226 |
| interaction(age, sex)30-39 years.Female | -0.083 | -0.622 | 0.457 | -0.300 | 0.764 |
| interaction(age, sex)40-49 years.Female | -0.302 | -0.766 | 0.161 | -1.278 | 0.201 |
| interaction(age, sex)50-59 years.Female | -0.810 | -1.258 | -0.362 | -3.543 | 0.000 |
| interaction(age, sex)60-64 years.Female | -0.787 | -1.237 | -0.337 | -3.428 | 0.001 |
| interaction(age, sex)65 years and over.Female | -0.603 | -1.035 | -0.170 | -2.733 | 0.006 |
| interaction(age, sex)teen.Female | -0.129 | -1.806 | 1.548 | -0.151 | 0.880 |
| interaction(bmi, diab)healthy weight.No | 1.380 | 0.085 | 2.675 | 2.089 | 0.037 |
| interaction(bmi, diab)Overweight.No | 1.085 | -0.204 | 2.373 | 1.650 | 0.099 |
| Standard errors: Robust |
fit9 <- update(fitstep, .~. + age:sex + bmi:diab)
publish(fit9)
#> Variable Units OddsRatio CI.95 p-value
#> OA Control Ref
#> OA 1.55 [1.42;1.69] < 1e-04
#> married not single Ref
#> single 0.98 [0.91;1.07] 0.7026897
#> race Non-white Ref
#> White 1.42 [1.18;1.70] 0.0001960
#> edu < 2ndary Ref
#> 2nd grad. 0.90 [0.81;1.00] 0.0566536
#> Other 2nd grad. 0.96 [0.83;1.12] 0.6183383
#> Post-2nd grad. 0.92 [0.84;1.01] 0.0807393
#> income $29,999 or less Ref
#> $30,000-$49,999 0.74 [0.67;0.81] < 1e-04
#> $50,000-$79,999 0.64 [0.58;0.71] < 1e-04
#> $80,000 or more 0.57 [0.50;0.65] < 1e-04
#> phyact Active Ref
#> Inactive 1.21 [1.10;1.34] 0.0001349
#> Moderate 1.08 [0.97;1.21] 0.1760803
#> fruit 0-3 daily serving Ref
#> 4-6 daily serving 0.94 [0.86;1.03] 0.1892549
#> 6+ daily serving 1.10 [0.98;1.23] 0.1142759
#> bp No Ref
#> Yes 2.37 [2.18;2.57] < 1e-04
#> doctor No Ref
#> Yes 1.71 [1.45;2.01] < 1e-04
#> stress Not too stressed Ref
#> stressed 1.29 [1.18;1.42] < 1e-04
#> smoke Never smoker Ref
#> Current smoker 1.16 [1.04;1.30] 0.0085960
#> Former smoker 1.19 [1.09;1.31] 0.0002579
#> drink Never drank Ref
#> Current drinker 0.81 [0.68;0.97] 0.0227934
#> Former driker 1.12 [0.93;1.35] 0.2264702
#> age(20-29 years): sex(Male vs Female) 0.97 [0.64;1.48] 0.8945322
#> age(30-39 years): sex(Male vs Female) 1.06 [0.75;1.49] 0.7583565
#> age(40-49 years): sex(Male vs Female) 1.32 [1.07;1.62] 0.0091527
#> age(50-59 years): sex(Male vs Female) 2.18 [1.85;2.58] < 1e-04
#> age(60-64 years): sex(Male vs Female) 2.14 [1.80;2.53] < 1e-04
#> age(65 years and over): sex(Male vs Female) 1.78 [1.58;1.99] < 1e-04
#> age(teen): sex(Male vs Female) 1.11 [0.22;5.62] 0.9033924
#> sex(Female): age(30-39 years vs 20-29 years) 1.24 [0.87;1.77] 0.2276609
#> sex(Female): age(40-49 years vs 20-29 years) 2.35 [1.75;3.16] < 1e-04
#> sex(Female): age(50-59 years vs 20-29 years) 3.94 [2.95;5.27] < 1e-04
#> sex(Female): age(60-64 years vs 20-29 years) 6.25 [4.66;8.39] < 1e-04
#> sex(Female): age(65 years and over vs 20-29 years) 11.37 [8.60;15.02] < 1e-04
#> sex(Female): age(teen vs 20-29 years) 0.44 [0.11;1.69] 0.2320840
#> sex(Male): age(30-39 years vs 20-29 years) 1.35 [0.89;2.05] 0.1599938
#> sex(Male): age(40-49 years vs 20-29 years) 3.18 [2.21;4.58] < 1e-04
#> sex(Male): age(50-59 years vs 20-29 years) 8.85 [6.24;12.56] < 1e-04
#> sex(Male): age(60-64 years vs 20-29 years) 13.73 [9.61;19.61] < 1e-04
#> sex(Male): age(65 years and over vs 20-29 years) 20.77 [14.59;29.57] < 1e-04
#> sex(Male): age(teen vs 20-29 years) 0.50 [0.18;1.37] 0.1769155
#> bmi(Underweight): diab(Yes vs No) 5.72 [1.59;20.63] 0.0076561
#> bmi(healthy weight): diab(Yes vs No) 1.44 [1.19;1.75] 0.0002221
#> bmi(Overweight): diab(Yes vs No) 1.93 [1.70;2.20] < 1e-04
#> diab(No): bmi(healthy weight vs Underweight) 0.97 [0.76;1.25] 0.8394972
#> diab(No): bmi(Overweight vs Underweight) 0.97 [0.76;1.25] 0.8400722
#> diab(Yes): bmi(healthy weight vs Underweight) 0.25 [0.07;0.87] 0.0302066
#> diab(Yes): bmi(Overweight vs Underweight) 0.33 [0.09;1.17] 0.0852377basic.model <- eval(fit5$call[[2]])
basic.model
#> I(CVD == "event") ~ OA + age + sex
#> attr(,"variables")
#> list(I(CVD == "event"), OA, age, sex)
#> attr(,"factors")
#> OA age sex
#> I(CVD == "event") 0 0 0
#> OA 1 0 0
#> age 0 1 0
#> sex 0 0 1
#> attr(,"term.labels")
#> [1] "OA" "age" "sex"
#> attr(,"order")
#> [1] 1 1 1
#> attr(,"intercept")
#> [1] 1
#> attr(,"response")
#> [1] 1
#> attr(,".Environment")
#> <environment: R_GlobalEnv>
#> attr(,"predvars")
#> list(I(CVD == "event"), OA, age, sex)
#> attr(,"dataClasses")
#> I(CVD == "event") OA age sex
#> "logical" "factor" "factor" "factor"
#> (weights)
#> "numeric"
aic.int.model <- eval(fit9$call[[2]])
aic.int.model
#> I(CVD == "event") ~ OA + age + sex + married + race + edu + income +
#> bmi + phyact + fruit + bp + diab + doctor + stress + smoke +
#> drink + age:sex + bmi:diabSaving data
Saves the final regression models for future use.
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