1. EHS 655 Lecture 14: Linear and logistic regression, task-based assessment

2. What we’ll cover today Robust linear regression with R2
Prediction with linear regression
Logistic regression modeling

3. Linear regression Robust regression with R2 Download rregfit
Download rregfit
Stata: rreg depvar indepvar rregfit

4. Regression - predict
Runs a regression model and saves the predicted values for each individual
i.e. can use regression to predict TWA based on job title, gender, perceived noise, etc.
Linear regression
Stata: rreg depvar indepvar1, cluster(idvar) predict fittedvar
Logistic regression
Stata: logistic depvar indepvar1, cluster(idvar) predict fittedvar

5. EXPOSURE MODELING Logistic regression Task-based estimation
Will use this in our analyses
Task-based estimation
May use this in our analysis

6. Binary logistic regression
Consider binary categorical (not continuous) outcome
Want to know probability of outcome
Described by odds ratio
Odds of event occurring, [p / (1-p)], where p is probability
Note that Stata will give you log odds or odds ratio (OR)
Assumptions similar to linear regression
e.g., independent observations, equal variance
Example: odds of TWA exposure >85 dBA

7. Binary logistic regression
Assumes outcome categorical and binary (i.e., 0 or 1)
0 = negative outcome, 1 = positive outcome
Predictor variables
Cannot be nominal variables unless “i.” function used
Continuous variables okay
Ordinal variables okay
“vce(robust)” accounts for mild assumption violations
Stata: logistic depvar indepvar, vce(robust)

8. Binary logistic regression
We model log odds
Where
Xi is a continuous variable
Xi=0, log odds = β0
Xi=x, log odds = β0 + β1x
Xi=x+1, log odds = β0 + β1x + β1

9. Binary logistic regression
Interpreting odds
Where
Xi=0, odds = eβ0
Xi=x, odds = eβ0 + eβ1x
Xi=x+1, odds = eβ0 + eβ1x + eβ1
For groups varying by 1 unit, odds = eβ1

10. Interpreting logistic regression results
Odds ratio when predictor = 0
Exponentiate intercept if using log odds: eβ0
(Otherwise have Stata output odds ratio)
Odds ratio between predictors differing by one unit
Exponentiate slope from regression: eβ1
Compare nested models with log likelihood score
E.g., model with variables 1 and 2 vs variable 1 alone; cannot compare variables 1 vs 2

11. Binary logistic regression
Interpreting model output
p-value for chi-square (aka likelihood ratio)
Test that all estimated coefficients equal zero
Test of whole model
Pseudo R2 (aka likelihood ratio index)
(log likelihood full model/log likelihood intercept-only model)
Log pseudolikelihood
Smaller value = better model fit

12. Binary logistic regression
Logistic regression with repeated measures
Stata: logistic depvar indepvar, cluster(idvar) or

13. Multiple logistic regression
Like simple logistic regression
But with 2 or more predictors
Stata: logistic depvar indepvar1 indepvar2, vce(robust)

14. Repeated measures logistic regression
Use if you have
Binary outcome
Predictor measured repeatedly for each subject
And want to
Run logistic regression that accounts for multiple (i.e., correlated) measures from single subjects
Stata: logistic depvar indepvar, cluster(idvar)

15. Multinominal logistic regression
Use if dependent variable is more than 2 categories, but not continuous
E.g., low, medium, high exposure
E.g., no, low, medium, severe health impact
Not expecting this level of sophistication in your analyses…but
Example: create 3-level ordinal exposure variable from TWA
Stata: mlogit depvar indepvar, or vce(robust)

16. Task-based exposure estimation
Develop exposure model based not on personal characteristics or grouping strategy, but on tasks
Assume task directly or indirectly determines exposure
Create estimates of personal exposure
Example: industry where tasks vary widely within groups
Where
T = total duration, t = duration of task n, f = frequency of task n, C = intensity of task n

17. Illustration of task-based approach

18. Task-based assessment
Can work better than other approaches
Neitzel et al, 2011

19. Task-based assessment for noise: example of implementation
Ignacio and Bullock, AIHA, 2006

20. Task-based assessment
Complicated
First, evaluate task-specific exposure levels
Then apply exposure levels to individual task durations and frequencies
Combination yields personal exposure estimate
We don’t always have information about all tasks person performs; may instead focus on
Longest task
Most frequent task
Task with highest exposure

21. (Pseudo) task-based estimation
What about our dataset?
To do task-based estimation right, we’d need info on all tasks performed, levels, and durations
We just have primary task performed
Stata: rreg depvar indepvar1 indepvar2 predict fitted