Author:
Yunbin Peng
Data set:
Audiometry & Demographic from NHANES 2005-2006 survey
https://wwwn.cdc.gov/Nchs/Nhanes/2005-2006/DEMO_D.XPT
https://wwwn.cdc.gov/Nchs/Nhanes/2005-2006/AUX_D.XPT
Description:
This script use linear regression function and lme4 package (for mixed model) in R to investigate how age, age group, gender affect hearing using NHANES survey.
library(sas7bdat)
library(lme4)## Loading required package: Matrixdata = read.sas7bdat("datalong.sas7bdat")
# create categorical variables
data$GENDER = factor(data$GENDER)
data$AGEGROUP = factor(data$AGEGROUP)
data$FREQUENCY = factor(data$FREQUENCY)
data$RIGHTEAR = factor(data$RIGHTEAR)
summary(data)## SEQN GENDER AGE AGEGROUP RIGHTEAR FREQUENCY
## Min. :31129 0:18662 Min. :12.00 0:27986 0:18634 500 :5324
## 1st Qu.:33673 1:18606 1st Qu.:14.00 1: 9282 1:18634 1000:5324
## Median :36210 Median :17.00 2000:5324
## Mean :36226 Mean :30.92 3000:5324
## 3rd Qu.:38781 3rd Qu.:19.00 4000:5324
## Max. :41469 Max. :85.00 6000:5324
## 8000:5324
## RESULT
## Min. :-10.00
## 1st Qu.: 5.00
## Median : 10.00
## Mean : 16.71
## 3rd Qu.: 20.00
## Max. :120.00
## # subset Right Ear Frequency 1000Hz
R1K = subset(data, (data$RIGHTEAR == 1) & (data$FREQUENCY == 1000))model1 = lm(RESULT ~ GENDER*AGEGROUP, data = R1K)
summary(model1)##
## Call:
## lm(formula = RESULT ~ GENDER * AGEGROUP, data = R1K)
##
## Residuals:
## Min 1Q Median 3Q Max
## -28.758 -5.398 -0.398 4.602 84.602
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.3982 0.3372 16.011 < 2e-16 ***
## GENDER1 -0.1499 0.4750 -0.316 0.752326
## AGEGROUP1 20.2177 0.6666 30.329 < 2e-16 ***
## GENDER1:AGEGROUP1 3.2919 0.9521 3.457 0.000554 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.62 on 2658 degrees of freedom
## Multiple R-squared: 0.4433, Adjusted R-squared: 0.4427
## F-statistic: 705.5 on 3 and 2658 DF, p-value: < 2.2e-16Since coefficient for interaction term (GENDER1:AGEGROUP1) is significant, there is a significant interaction between age group and gender in determining how well an individual hears.
model2 = lm(RESULT ~ AGE + AGEGROUP + GENDER, data = R1K)
summary(model2)##
## Call:
## lm(formula = RESULT ~ AGE + AGEGROUP + GENDER, data = R1K)
##
## Residuals:
## Min 1Q Median 3Q Max
## -30.110 -5.957 -0.957 4.236 86.017
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.94926 1.01388 -5.868 4.96e-09 ***
## AGE 0.70947 0.06266 11.322 < 2e-16 ***
## AGEGROUP1 -22.11708 3.90941 -5.657 1.70e-08 ***
## GENDER1 0.55491 0.40313 1.376 0.169
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.4 on 2658 degrees of freedom
## Multiple R-squared: 0.4665, Adjusted R-squared: 0.4659
## F-statistic: 774.8 on 3 and 2658 DF, p-value: < 2.2e-16Even after controlling for age group, the coefficient of age is still significant.
model3 = lm(RESULT ~ AGE + AGE*AGEGROUP + AGEGROUP, data = R1K)
summary(model3)##
## Call:
## lm(formula = RESULT ~ AGE + AGE * AGEGROUP + AGEGROUP, data = R1K)
##
## Residuals:
## Min 1Q Median 3Q Max
## -31.968 -5.394 -0.394 4.606 84.889
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.1295 1.5821 1.978 0.048 *
## AGE 0.1416 0.1010 1.401 0.161
## AGEGROUP1 -57.8639 6.3066 -9.175 < 2e-16 ***
## AGE:AGEGROUP1 0.9158 0.1280 7.152 1.1e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.3 on 2658 degrees of freedom
## Multiple R-squared: 0.4762, Adjusted R-squared: 0.4756
## F-statistic: 805.6 on 3 and 2658 DF, p-value: < 2.2e-16Since the coefficient of AGE*AGEGROUP (0.9158) is statistically significant, the effect of age is different for different age groups.
mixmodel1 = lmer(RESULT ~ GENDER*AGEGROUP + (1|FREQUENCY) + (1|RIGHTEAR), data = data)
summary(mixmodel1)## Linear mixed model fit by REML ['lmerMod']
## Formula: RESULT ~ GENDER * AGEGROUP + (1 | FREQUENCY) + (1 | RIGHTEAR)
## Data: data
##
## REML criterion at convergence: 302935.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0705 -0.5764 -0.0207 0.4704 6.5333
##
## Random effects:
## Groups Name Variance Std.Dev.
## FREQUENCY (Intercept) 28.16479 5.3071
## RIGHTEAR (Intercept) 0.07585 0.2754
## Residual 198.23711 14.0797
## Number of obs: 37268, groups: FREQUENCY, 7; RIGHTEAR, 2
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 7.5461 2.0188 3.74
## GENDER1 -0.8728 0.1683 -5.18
## AGEGROUP1 41.3207 0.2362 174.93
## GENDER1:AGEGROUP1 -5.6848 0.3374 -16.85
##
## Correlation of Fixed Effects:
## (Intr) GENDER1 AGEGRO
## GENDER1 -0.042
## AGEGROUP1 -0.030 0.359
## GENDER1:AGE 0.021 -0.499 -0.700The coefficient of GENDER1:AGEGROUP1 is significant, indicating there is significant interaction between age group and gender.
mixmodel2 = lmer(RESULT ~ AGE + AGEGROUP + GENDER + (1|FREQUENCY) + (1|RIGHTEAR), data = data)
summary(mixmodel2)## Linear mixed model fit by REML ['lmerMod']
## Formula:
## RESULT ~ AGE + AGEGROUP + GENDER + (1 | FREQUENCY) + (1 | RIGHTEAR)
## Data: data
##
## REML criterion at convergence: 302157.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0516 -0.5685 -0.0335 0.4842 6.4031
##
## Random effects:
## Groups Name Variance Std.Dev.
## FREQUENCY (Intercept) 28.16584 5.3071
## RIGHTEAR (Intercept) 0.07607 0.2758
## Residual 194.11650 13.9326
## Number of obs: 37268, groups: FREQUENCY, 7; RIGHTEAR, 2
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -3.11404 2.04783 -1.52
## AGE 0.73791 0.02245 32.88
## AGEGROUP1 -7.17565 1.40038 -5.12
## GENDER1 -2.40699 0.14441 -16.67
##
## Correlation of Fixed Effects:
## (Intr) AGE AGEGRO
## AGE -0.169
## AGEGROUP1 0.165 -0.993
## GENDER1 -0.031 -0.025 0.027Coefficient of AGE is significant, hence after controlling for age group and gender, age is still important as a variable.
mixmodel3 = lmer(RESULT ~ AGE + AGE*AGEGROUP + AGEGROUP + (1|FREQUENCY) + (1|RIGHTEAR), data = data)
summary(mixmodel3)## Linear mixed model fit by REML ['lmerMod']
## Formula: RESULT ~ AGE + AGE * AGEGROUP + AGEGROUP + (1 | FREQUENCY) +
## (1 | RIGHTEAR)
## Data: data
##
## REML criterion at convergence: 301978.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.1109 -0.5832 -0.0369 0.4631 6.6221
##
## Random effects:
## Groups Name Variance Std.Dev.
## FREQUENCY (Intercept) 28.16599 5.3072
## RIGHTEAR (Intercept) 0.07612 0.2759
## Residual 193.17187 13.8986
## Number of obs: 37268, groups: FREQUENCY, 7; RIGHTEAR, 2
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 5.38514 2.09459 2.571
## AGE 0.11109 0.03643 3.049
## AGEGROUP1 -45.10954 2.27434 -19.834
## AGE:AGEGROUP1 0.99184 0.04618 21.480
##
## Correlation of Fixed Effects:
## (Intr) AGE AGEGRO
## AGE -0.269
## AGEGROUP1 -0.068 0.248
## AGE:AGEGROU 0.213 -0.789 -0.789Coefficient of AGE:AGEGROUP1 is significant, so effect of age is different for different age groups.