betareg

Dependency of Anxiety on Stress

Description

Stress and anxiety among nonclinical women in Townsville, Queensland, Australia.

Usage

data("StressAnxiety", package = "betareg")

Format

A data frame containing 166 observations on 2 variables.

stress: score, linearly transformed to the open unit interval (see below).
anxiety: score, linearly transformed to the open unit interval (see below).

Details

Both variables were assess on the Depression Anxiety Stress Scales, ranging from 0 to 42. Smithson and Verkuilen (2006) transformed these to the open unit interval (without providing details about this transformation).

Source

Example 2 from Smithson and Verkuilen (2006) supplements.

References

Smithson M, Verkuilen J (2006). A Better Lemon Squeezer? Maximum-Likelihood Regression with Beta-Distributed Dependent Variables. Psychological Methods, 11(7), 54–71.

Examples

library("betareg")

data("StressAnxiety", package = "betareg")
StressAnxiety <- StressAnxiety[order(StressAnxiety$stress),]

## Smithson & Verkuilen (2006, Table 4)
sa_null <- betareg(anxiety ~ 1 | 1,
  data = StressAnxiety, hessian = TRUE)
sa_stress <- betareg(anxiety ~ stress | stress,
  data = StressAnxiety, hessian = TRUE)
summary(sa_null)


Call:
betareg(formula = anxiety ~ 1 | 1, data = StressAnxiety, hessian = TRUE)

Quantile residuals:
    Min      1Q  Median      3Q     Max 
-0.8377 -0.8377 -0.4467  0.6217  3.2396 

Coefficients (mean model with logit link):
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) -2.24396    0.09879  -22.71   <2e-16 ***

Phi coefficients (precision model with log link):
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)    1.796      0.123    14.6   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Type of estimator: ML (maximum likelihood)
Log-likelihood: 239.4 on 2 Df
Number of iterations in BFGS optimization: 9

summary(sa_stress)


Call:
betareg(formula = anxiety ~ stress | stress, data = StressAnxiety, hessian = TRUE)

Quantile residuals:
    Min      1Q  Median      3Q     Max 
-2.0119 -0.7953 -0.1833  0.5658  3.1141 

Coefficients (mean model with logit link):
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  -4.0237     0.1442  -27.90   <2e-16 ***
stress        4.9414     0.4409   11.21   <2e-16 ***

Phi coefficients (precision model with log link):
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)   3.9608     0.2511  15.776  < 2e-16 ***
stress       -4.2733     0.7532  -5.674  1.4e-08 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Type of estimator: ML (maximum likelihood)
Log-likelihood:   302 on 4 Df
Pseudo R-squared: 0.4748
Number of iterations in BFGS optimization: 16

AIC(sa_null, sa_stress)

          df       AIC
sa_null    2 -474.8960
sa_stress  4 -595.9202

1 - as.vector(logLik(sa_null)/logLik(sa_stress))

[1] 0.207021

## visualization
attach(StressAnxiety)
plot(jitter(anxiety) ~ jitter(stress),
  xlab = "Stress", ylab = "Anxiety",
  xlim = c(0, 1), ylim = c(0, 1))
lines(lowess(anxiety ~ stress))
lines(fitted(sa_stress) ~ stress, lty = 2)
lines(fitted(lm(anxiety ~ stress)) ~ stress, lty = 3)
legend("topleft", c("lowess", "betareg", "lm"), lty = 1:3, bty = "n")

detach(StressAnxiety)

## see demo("SmithsonVerkuilen2006", package = "betareg") for more details