ASRB Agricultural Research Service (ARS) - Agricultural Statistics scientist · India · Agricultural Scientists Recruitment Board (ICAR)
Original practice questions written to the published syllabus · not past papersModels for counts, proportions and categories: contingency tables, the exponential-family GLM with its link functions, logistic and Poisson regression, log-linear models, overdispersion, ordinal outcomes and generalised linear mixed models, applied to germination, mortality, pest counts and adoption data.
In the exams: AICE-JRF Ag Stat Unit 2 'contingency tables, log linear models' (heavy); GATE DA logistic regression (present); light in UPSC ISS
How our questions for ASRB Agricultural Research Service spread across the units of Categorical Data Analysis & Generalized Linear Models. Difficulty: 7 easy, 30 medium, 7 hard.
| Logistic regression for binary and binomial data | 6 | |
| Zero-inflated and hurdle models | 6 | |
| Poisson regression for counts | 5 | |
| Ordinal and multinomial logistic models | 5 | |
| Generalized linear mixed models | 5 | |
| Overdispersion: quasi-likelihood and negative binomial models | 4 | |
| Contingency tables: association, odds ratios and tests | 3 | |
| Exponential family and the generalized linear model | 3 | |
| Link functions, deviance and iteratively reweighted least squares | 3 | |
| Model checking: residuals and goodness of fit | 3 | |
| Log-linear models for multi-way tables | 1 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
A germination model has residual deviance 31.2 on 16 df, and dropping treatments raises it by 21.6 on 3 df. Taking the dispersion as φ̂ = 31.2/16, what is the quasi-likelihood F statistic?
C. 3.69 on (3, 16) df
φ̂ = 1.95; F = (21.6/3)/1.95 = 3.69. 7.20 ignores overdispersion; 11.08 forgets to divide by the 3 df.
Further reading: McCullagh and Nelder, Generalized Linear Models; Agresti, Categorical Data Analysis; Dobson and Barnett, An Introduction to Generalized Linear Models
A logistic regression fails to converge, with one coefficient and its standard error growing very large. What is the likely cause and remedy?
C. Separation; use Firth's penalised likelihood
Under complete or quasi-complete separation the MLE is infinite, so estimates diverge; Firth's bias-reduced likelihood or exact methods give finite estimates. More iterations or another link do not help.
Further reading: McCullagh and Nelder, Generalized Linear Models; Agresti, Categorical Data Analysis; Dobson and Barnett, An Introduction to Generalized Linear Models
Trap A catches 42 thrips in 6 days; trap B catches 50 in 10 days. With log(days) as offset, what is the estimated log rate ratio A versus B?
B. 0.336
Rates are 7.0 and 5.0 per day, ratio 1.4, log 1.4 = 0.336. log(42/50) = −0.174 ignores exposure and wrongly favours trap B.
Further reading: McCullagh and Nelder, Generalized Linear Models; Agresti, Categorical Data Analysis; Dobson and Barnett, An Introduction to Generalized Linear Models
Lesion counts per leaf are mostly 0 to 3. Why is a Poisson (or negative binomial) GLM better than ANOVA on log(count + 1)?
A. It needs no arbitrary added constant
With small counts, log(y + 1) depends on the arbitrary constant and does not stabilise variance well; the count GLM uses the right distribution and link. Overdispersion still needs checking.
Further reading: McCullagh and Nelder, Generalized Linear Models; Agresti, Categorical Data Analysis; Dobson and Barnett, An Introduction to Generalized Linear Models
How do the variance functions of quasi-Poisson and NB2 negative binomial models differ?
D. Linear in μ versus quadratic in μ
The shapes differ, so the models weight large counts differently; a plot of squared residuals against fitted means helps choose.
Further reading: McCullagh and Nelder, Generalized Linear Models; Agresti, Categorical Data Analysis; Dobson and Barnett, An Introduction to Generalized Linear Models
In a hurdle model for pest counts, where do zeros come from?
C. Only from the binary part
The count part is zero-truncated, so every zero comes from the binary zero-versus-positive model. In zero-inflated models zeros come from both sources.
Further reading: McCullagh and Nelder, Generalized Linear Models; Agresti, Categorical Data Analysis; Dobson and Barnett, An Introduction to Generalized Linear Models
Many fields have no pest because it has not yet arrived, while infested fields have Poisson-like counts that can also be zero. Which model matches this story?
D. Zero-inflated model
Two sources of zeros, structural (pest absent) and sampling (present but none caught), is the zero-inflated story. A hurdle model assumes all zeros come from one binary process.
Further reading: McCullagh and Nelder, Generalized Linear Models; Agresti, Categorical Data Analysis; Dobson and Barnett, An Introduction to Generalized Linear Models
In a zero-inflated negative binomial model, which part's predictors explain the probability of a structural zero?
D. A logistic model for π
ZINB has two linear predictors: logit π for structural zeros and log μ for the counts; the same or different covariates can enter each.
Further reading: McCullagh and Nelder, Generalized Linear Models; Agresti, Categorical Data Analysis; Dobson and Barnett, An Introduction to Generalized Linear Models
How can an observation-level random effect help in a Poisson GLMM?
A. It absorbs overdispersion
A normal random effect for each observation makes the counts a Poisson-lognormal mixture, with variance exceeding the mean.
Further reading: McCullagh and Nelder, Generalized Linear Models; Agresti, Categorical Data Analysis; Dobson and Barnett, An Introduction to Generalized Linear Models
A binomial GLMM reports a block variance estimate of exactly zero. How should this be treated?
B. A singular fit, reported as such
Boundary estimates are common with few levels; they mean the data cannot distinguish block variation from zero, not that it is absent.
Further reading: McCullagh and Nelder, Generalized Linear Models; Agresti, Categorical Data Analysis; Dobson and Barnett, An Introduction to Generalized Linear Models
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