Measurement Error & Mixed Models

Question 1

Sources of measurement error (ME)

Answer 1

• Measurement imprecision in the field or in the lab (length, weight, blood pressure, etc.).
• incomplete or inaccurate observations (e.g., self-reported dietary aspects, health history).
• Rounding error, digit preference.
• Classification error (e.g., exposure or disease classification).

-> assumption is that x is measured without error for corr, regr, anova, glm

If this assumption is violated:
- biased estimates
- loss of power
- incorrect variable importance
- masks important features of the data -> making graphical model inspection difficult

Question 2

Measurement error

Answer 2

Xi = correct unobserved variable
Wi = observed variable with error
-> slope is flacher

Question 3

How to correct ME

Answer 3

Need error model & error model parameters
-> take repeated measurements to estimate error variance

Attenuation factor lambda = sdx^2 / (sdx^2 + sdu^2)

Question 4

SIMEX

Answer 4

Simulation phase:
- error in the data is progressively aggravated in order to determine how the model parameter of interest is affected.

Extrapolation phase:
- simulated trend is then extrapolated back to a hypothetical error-free value of the model parameter.

Question 5

Practical advice

Answer 5

• Think about measurement error before you start collecting your data.
• Ideally, take repeated measurements
• Figure out if error is a problem and what the bias in your parameters might be. You might need simulations to find out.
• If needed, model the error. Seek help from a statistician!

Question 6

Mixed models

Answer 6

Not each observation is independant datapoint!!
Taking average would destroy a lot of data

Problem: Df not clear -> thats why significance tests of fixed effects are difficult when using mixed models

Question 7

Why not take average

Answer 7

1. To adjust estimates for imbalanced sampling.
2. Which average? (Mean/median/mode?)
3. Avoid false confidence. (Due to removing variance)
4. To study variation.
5. To adjust estimates for repeat sampling (sharing information)
6. To keep information.

Question 8

Fixed effects

Answer 8

Sex
Height
Weight
Size
…
-> Groups / levels are predetermined, of direct interest, repeatable

Question 9

Random effects

Answer 9

Individual
Nest
Family
-> Groups that are randomly sampled from a larger population of groups

Question 10

Mixed Models in R

Answer 10

Lmer()
Package: lme4

Question 11

Many or just one measure

Answer 11

• measurement of 1 RT spread more in direction of x axis
• slope of 1 RT less steep
• measurement of only 1 RT is morre variable than the mean of 5 RTs

Question 12

Why prefer a multilevel model rel to analysing averages?

Answer 12

• to avoid false confidence
• bc we would retain variation that may be of interest
• averaging would require an arbitrary decision about which average to use

Question 13

Why is ME in covariates of regression models problematic?

Answer 13

• parameter estimates may be biased
• it is a fundamental assumption of regression models that covariates do not contain any error
• it is much harder than to find patterns by visual inspection
• the p-values of the regression coefficients may be wrong