Questions on LMM #2

Question 1

True or false : A model is said to be a nested model if it is a special case of another model

Answer 1

True

Question 2

Describe the LR ratio test (formula, distribution)

Answer 2

1, 2 times difference in Loglikelihood
2. Follows a chi-square distribution, with number of degrees of freedom equals difference in number of parameters between the reference model and the nested model

Question 3

True or false : When doing the LRT, the nested model should differ in the number of fixed parameters or in the number of covariance parameters, but not in both

Answer 3

True

Question 4

True or false : If doing the LRT on fixed parameters, the REML fitting should be used

Answer 4

False, ML should be used, because REML is variant to a change in the parametrization of fixed effect. ML is invariant

Question 5

True or false : If doing the LRT on covariance parameters, the REML fitting should be used

Answer 5

True

Question 6

How we calculate the number of degrees of freedom for covariance parameters for different covariance structures?

Answer 6

1. The number of degrees of freedom depends on whether the values of the covariance parameters that are fixed in the nested model are at their boundaries in the parameter space
2. Boundary of Variance = 0
3. No boundaries for covariance (can be positive/negative)
4. If covariance parameters is not at their boundaries, then each parameter has 1 degree of freedom

Question 7

If the reference model has a random intercept and the nested model has nothing, what is the distribution of the LRT?

Answer 7

Equally-weighted average of 0 and 1 degree of freedom

Question 8

If the reference model has a random intercept and a random coefficient and the nested model only have a random intercept, what is the distribution of the LRT?

Answer 8

Equally-weighted average of 1 and 2 degrees of freedom

Question 9

Give me information about the t-test

Answer 9

1. It is for the fixed effect parameters
2. The test only require the reference model
3. Ho -: B = 0
4. Ha : B does not equal 0
5. t = B / se(B)
6. Because of random effects, number of df need to be approximated

Question 10

Give me information about F test

Answer 10

1. It is for the fixed effect parameters
2. The test only require the refence model
3. Used to test linear hypotheses about multilple fixed effects in LMM
4. Sattherwaite method is a method to adjust the number of df
5. Can use also the kenward-rogers method (Use the Sattherwaite but also modifies the estimated covariance matrix Vi to reflect the uncertainty in using Vi chapeau are a substitute of Vi
6. Focus on Type 1 and Type 3 F test

Question 11

Give me information about the Omnibus Wald test

Answer 11

1. Like F-test, can be used to to test linear hypotheses about multiple effects in LMM
2. For fixed effects
3. Only require the reference model

Question 12

Instead of LRT, what are the alternative test for covariance parameters?

Answer 12

1. Wald z-test

Question 13

Do we recommend Wald z-test for covariance parameters? Why?1

Answer 13

No.

1. The random factor must have a large number of unique values for the asymptomatic estimate to be a good approximation
2. The test is problematic when the null hypothesis puts the parameter at a boundary value

Question 14

What are the test for non-nested model?

Answer 14

1. AIC (lower the better)
2. BIC (lower the better)
   Formulas are in the document

Question 15

What are the 2 strategies we can use for building LMM?

Answer 15

1. .Top-down

2. Step-up

Question 16

Tell me more about the top-down strategy for building LMM (Steps)

Answer 16

1. Start with a well-specified mean structure for the model
   - -­> Include all fixed effects that may be relevant
2. Include all random effects that may be relevant. Select a structure for D
3. Select a structure for RI
4. Reduce the model

Question 17

Tell me more about the step-up strategy for building LMM (steps)

Answer 17

1. Start with an unconditional Level 1 model for the data
2. Add level 1 covariates, and consider adding random coefficients for level 2 variables with those level 1 covariates
3. Add level 2 covariates

Question 18

What is the advantage of the step-down approach?

Answer 18

Covariances can be thought of as measuring variances rather than as measuring variation due to omitted fixed effects

Question 19

What is the advantage of the step-up approach?

Answer 19

The effect of each covariate on reducing the variance can be viewed separately for each level

Question 20

True or false : Conditional residuals are correlated even if the true residuals are not

Answer 20

True!

Question 21

Explain what is standardized and studentized residuals

Answer 21

1. Residuals divided by their standard deviation

2. Residuals divided by their estimated standard deviation

Question 22

Explain what is Pearson residuals

Answer 22

Residuals divided by the estimated standard deviation of the dependant variable

Question 23

Explain what is internal studentization

Answer 23

Standard deviation of a residual is estimated using that residual

Question 24

Explain what is external studentization

Answer 24

The standard deviation of a residual is estimated excluding that residual

Question 25

Explain what is a influence diagnostics

Answer 25

Statistics that identify data that has a large influence on the data.

Question 26

True or false : The influence diagnostic are best used with the top-down strategy

Answer 26

True

Question 27

Enumerer les influence diagnostics

Answer 27

1. Likelihood distance 2. Cook D 3. Multivariate DFFITS 4. Change in precision of B or theta 5. PRESS

Question 28

True or false : Ui chapeau is the EBLUP predictor of u

Answer 28

True

Question 29

True or false : EBLUPs are also known as shrinkage estimators because they then to be closer to 0 than the estimated effects would be if they were computed by treating a random factor as if it were fixed

Answer 29

True

Question 30

What is the difference between Ui chapeau et B chapeau?

Answer 30

Ui chapeau is EBLUP | B chapeau is EBLUE

Question 31

SVP Aller voir les formules de EBLUP lorsqu'il y a plusieurs observations

Answer 31

OK

Question 32

What Aliasing means?

Answer 32

We can think of aliasing as an ambiguity that may occur in the specification of a parametric model, in which multiple parameter sets imply models that are indistinguishable from each other

Question 33

What are the 2 types of aliasing?

Answer 33

1. Intrinsic Aliasing : Aliasing attributable to the model formula specification (Excess parameters) 2. Extrinsic Aliasing : Aliasing attributable to the particular characteristic of a given data set

Question 34

True or false : Intrinsic aliasing is often referred as nonidentifiability and overparametrization

Answer 34

True