ASRB NET Linear Mixed Models, Variance Components & Spatial Analysis of Field Trials: practice questions

1 · Fixed, random and mixed models revisited · easy

In the mixed model y = X beta + Z u + e, with u ~ N(0, G) and e ~ N(0, R), what is the variance of y?

1. G + R
2. Z R Z' + G
3. Z G Z' + R
4. X G X' + R

2 · Fixed, random and mixed models revisited · medium

Which model suits germination counts per pot with random blocks?

1. A linear mixed model on the raw counts, whatever their distribution
2. An ordinary least squares model with no blocks
3. A generalised linear mixed model with a suitable link
4. A fixed-effects ANOVA on block totals

3 · Henderson's mixed-model equations; BLUE and BLUP · medium

In the mixed model, what is beta-hat from the mixed-model equations?

1. The BLUP of the random effects
2. The ML estimate of variance
3. The OLS estimate, ignoring the covariance matrix V
4. The BLUE of beta, equal to the GLS estimator

4 · Spatial analysis of field trials: nearest-neighbour and AR1 x AR1 models · easy

Why is spatial analysis used in field trials?

1. Fertility varies smoothly and irregularly, not only between blocks
2. Blocks are never useful in field trials
3. It removes the need for replication
4. Plots far apart are always more alike than adjacent plots in a block

5 · Trend and spline adjustment (e.g. SpATS approach) · medium

Can a spline surface and an AR1 x AR1 residual be combined in one model?

1. Only if the trial has a single row
2. Only when no genotypes or treatments are fitted in the model
3. No, they are mathematically incompatible
4. Yes, for large-scale trend plus local correlation

6 · Model selection with likelihood-ratio tests and information criteria · hard

Why is the naive chi-square test conservative when testing a variance component equal to zero?

1. Variance components are always large
2. REML likelihoods cannot be compared between any two models at all
3. The null value lies on the boundary of the parameter space
4. The chi-square has too many df

7 · Model selection with likelihood-ratio tests and information criteria · medium

Comparing AR(1) and Toeplitz residual structures with the same fixed effects, which tool is appropriate?

1. Bartlett's test on residuals
2. REML-based AIC or BIC
3. A t test on the variety means
4. ML-based F tests on fixed effects

8 · Model selection with likelihood-ratio tests and information criteria · medium

Why are replicate and block random terms usually kept even if not significant?

1. They always reduce AIC
2. They are required by all software
3. They reflect the randomisation of the design
4. They are fixed effects in disguise and are tested like treatments

9 · Maximum likelihood and REML · easy

What does REML stand for?

1. Repeated measures linear model
2. Restricted (residual) maximum likelihood
3. Random effects minimum loss
4. Regression estimate of mean level

10 · Henderson's mixed-model equations; BLUE and BLUP · easy

What does BLUP stand for?

1. Bayesian likelihood under priors
2. Best linear unbiased prediction
3. Balanced linear unit prediction
4. Block level uniform precision