Linear Mixed Models: An Introduction with Applications in Veterinary Research • Linear Mixed Models with Applications in Veterinary Research

Research

Overview

VetResearchLMM gives the data sets and every analysis of Duchateau, Janssen and Rowlands (1998), Linear Mixed Models. An Introduction with Applications in Veterinary Research (ILRI, Nairobi), with its own engine for linear mixed models that gives the results the book prints from SAS PROC MIXED and PROC GLM.

vlm_fit(): REML, ML or Type 3 (moment) estimation; random variance components, random coefficients (vlm_random(), VC or UN) and residual structures (vlm_repeated(): CS, AR(1), SP(POW), UN); the fixed-effects solution in the overparameterised coding; Type 3 or Type 1 tests with containment, residual, between-within, Satterthwaite or Kenward-Roger degrees of freedom; fit statistics;
vlm_lsmeans(), vlm_estimate(), vlm_contrast(): least-squares means with Tukey, Bonferroni or Sidak comparisons, estimates in the broad and narrow inference spaces, and F tests of contrasts;
vlm_blup(): best linear unbiased predictions of random effects;
vlm_ems(): the analysis of variance with expected mean squares and synthesised F tests;
vlm_compare(): information criteria and likelihood ratio tests of covariance structures;
vlm_interpret(), vlm_cite(), vlm_app(): plain-language interpretation, references and a shiny application in which every example of the book loads with one click.

The help pages ?Examp1.3.2 to ?Examp3.3 give the SAS program of each example with the same analysis in R. The package reproduces 115 of the 116 numbers of the book that it checks; the other one is printed truncated (3.685 for 3.6855). Version 2.0.0 keeps the data sets, the help topics and emmeans_mixed_model() and report_mixed_model() of version 1.1.0, adds the data sets of Examples 1.2.2, 1.2.3 and 1.2.6, and corrects three typing errors in ex33.

Installation

install.packages("VetResearchLMM")
# development version
# install.packages("remotes")
remotes::install_github("myaseen208/VetResearchLMM")

Quick start

The split-plot experiment of Example 1.2.5 (drugs given to herds within regions, doses to animals within herds):

library(VetResearchLMM)
fm <-
  vlm_fit(
      fixed    = Pcv ~ Drug + dose + Drug:dose
    , data     = ex125
    , random   = ~ Region + Region:Drug
    , repeated = NULL
    , method   = c("REML", "ML", "Type3")
    , ddfm     = "satterth"
    , type     = 3
    , class    = NULL
    , bound    = TRUE
    , control  = list()
    )
fm

Linear mixed model: Pcv ~ Drug + dose + Drug:dose
Estimation: REML; denominator df: satterth; converged after 6 iterations
Random: Region; Region:Drug

Covariance parameter estimates
   parameter subject estimate     se      z      p
      Region            5.151  3.739  1.378 0.0842
 Region:Drug           0.3870  1.022 0.3788 0.3524
    Residual            2.096 0.9375  2.236 0.0127

Fit statistics
                statistic   value
    -2 Res Log Likelihood 92.3786
  AIC (smaller is better) 98.3786
 AICC (smaller is better) 99.8786
  BIC (smaller is better) 101.366

Solution for fixed effects
      effect     level estimate     se    df      t        p
 (Intercept)              17.13  1.128 8.208  15.19  < 1e-04
        Drug   BERENIL    7.150 0.9098 11.82  7.859  < 1e-04
        Drug   samorin        0                            .
        dose         h    4.350 0.8359 10.00  5.204 0.000399
        dose         l        0                            .
   Drug:dose BERENIL h   -3.183  1.182 10.00 -2.693 0.022594
   Drug:dose BERENIL l        0                            .
   Drug:dose samorin h        0                            .
   Drug:dose samorin l        0                            .

Type 3 tests of fixed effects
    effect num_df den_df     F        p
      Drug      1  5.000 64.58 0.000483
      dose      1  10.00 21.78 0.000886
 Drug:dose      1  10.00 7.251 0.022594

Sources: Duchateau, Janssen and Rowlands (1998); Patterson and Thompson (1971);
Gilmour, Thompson and Cullis (1995); Littell, Milliken, Stroup and Wolfinger
(1996); Satterthwaite (1946); Giesbrecht and Burns (1985); Fai and Cornelius
(1996). Full references: vlm_cite(x).

vlm_interpret(
    x     = fm
  , alpha = 0.05
  , top   = 3L
  )

Linear mixed model

Pcv ~ Drug + dose + Drug:dose, fitted by REML with 3 covariance parameters.

Findings:
- Of the total variance 7.63, 67.5% is due to Region, 5.1% is due to
  Region:Drug, 27.5% is due to the residual (within) variation.
- Significant at the 0.05 level: Drug (F = 64.6 on 1 and 5 df, p = 0.00048);
  dose (F = 21.8 on 1 and 10 df, p = 0.00089); Drug:dose (F = 7.25 on 1 and
  10 df, p = 0.023).

Recommendations:
- The interaction Drug:dose is significant: compare the levels of one factor
  within each level of the other (vlm_lsmeans() of the interaction, or
  vlm_estimate()) rather than main-effect means.
- Report means with standard errors in the broad inference space
  (vlm_lsmeans()); use vlm_estimate() with `random` for the narrow space of
  the observed levels.

Sources:
- Duchateau, L., Janssen, P. and Rowlands, G. J. (1998). Linear Mixed Models.
  An Introduction with Applications in Veterinary Research. International
  Livestock Research Institute, Nairobi. ISBN 92-9146-038-9.
- Patterson, H. D. and Thompson, R. (1971). Recovery of inter-block
  information when block sizes are unequal. Biometrika, 58(3), 545-554.
  doi:10.1093/biomet/58.3.545
- Gilmour, A. R., Thompson, R. and Cullis, B. R. (1995). Average information
  REML: an efficient algorithm for variance parameter estimation in linear
  mixed models. Biometrics, 51(4), 1440-1450. doi:10.2307/2533274
- Littell, R. C., Milliken, G. A., Stroup, W. W. and Wolfinger, R. D. (1996).
  SAS System for Mixed Models. SAS Institute, Cary, NC.
- Satterthwaite, F. E. (1946). An approximate distribution of estimates of
  variance components. Biometrics Bulletin, 2(6), 110-114.
  doi:10.2307/3002019
- Giesbrecht, F. G. and Burns, J. C. (1985). Two-stage analysis based on a
  mixed model: large-sample asymptotic theory and small-sample simulation
  results. Biometrics, 41(2), 477-486. doi:10.2307/2530872
- Fai, A. H.-T. and Cornelius, P. L. (1996). Approximate F-tests of multiple
  degree of freedom hypotheses in generalized least squares analyses of
  unbalanced split-plot experiments. Journal of Statistical Computation and
  Simulation, 54(4), 363-378. doi:10.1080/00949659608811740

lm1 <-
  vlm_lsmeans(
      fit    = fm
    , specs  = ~ Drug:dose
    , at     = NULL
    , diff   = TRUE
    , adjust = "tukey"
    , level  = 0.95
    )
plot(x = lm1)

Learn more

Vignettes: browseVignettes("VetResearchLMM"), starting with VetResearchLMM_01_getting_started; PDF versions on the site.
Site: https://myaseen208.com/VetResearchLMM/
Notation: vlm_notation()
References of the methods behind a result: vlm_cite()

Citation

Yaseen M, Duchateau L, Janssen P, Rowlands J (2026). _VetResearchLMM:
Linear Mixed Models: An Introduction with Applications in Veterinary
Research_. R package version 2.0.0,
<https://CRAN.R-project.org/package=VetResearchLMM>.

BibTeX:

@Manual{VetResearchLMM,
  title = {{VetResearchLMM}: Linear Mixed Models: An Introduction with Applications in Veterinary Research},
  author = {Muhammad Yaseen and Luc Duchateau and Paul Janssen and John Rowlands},
  year = {2026},
  note = {R package version 2.0.0},
  url = {https://CRAN.R-project.org/package=VetResearchLMM},
}

Please also cite the book: citation("VetResearchLMM") lists it with the package, and vlm_cite(x) gives the references of a single result.

VetResearchLMM: Linear Mixed Models with Applications in Veterinary

Overview

Installation

Quick start

Learn more

Citation