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Linear mixed model of a multi-environment trial

Source: R/ge_model.R
ge_model.Rd

ge_model() fits the two-way model with interaction and random replicates within environments by restricted maximum likelihood (lme4::lmer()). Its residual variance is the error variance of the least-squares AMMI fit (ge_ammi(), which computes it in closed form).

Usage

ge_model(.data, .y, .gen, .env, .rep)

# Default S3 method
ge_model(.data, .y, .gen, .env, .rep)

Arguments

.data

a data frame with one row per plot.

.y, .gen, .env, .rep

the columns of the response, genotypes, environments and replicates: bare names, strings or vectors.

Value

The lmerMod object of lme4::lmer(Y ~ Env + Gen + Env:Gen + (1 | Env:Rep)).

Details

$$y_{ijl} = \mu + \delta_j + \tau_i + (\tau\delta)_{ij} + b_{l(j)} + e_{ijl}, \qquad b_{l(j)} \sim N(0, \sigma^2_b), \quad e_{ijl} \sim N(0, \sigma^2).$$ The package lme4 is needed (it is suggested, not required, since version 1.0.0).

References

Crossa, J., Perez-Elizalde, S., Jarquin, D., Cotes, J. M., Viele, K., Liu, G. and Cornelius, P. L. (2011). Bayesian estimation of the additive main effects and multiplicative interaction model. \emphCrop Science, \strong51(4), 1458–1469. \doi10.2135/cropsci2010.06.0343

Bates, D., Maechler, M., Bolker, B. and Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1–48. doi:10.18637/jss.v067.i01

See also

ge_ammi

Author

Muhammad Yaseen (myaseen208@gmail.com)

Examples

data(Maiz)
if (requireNamespace("lme4", quietly = TRUE)) {
  fm <-
    ge_model(
        .data = Maiz
      , .y    = y
      , .gen  = entry
      , .env  = site
      , .rep  = rep
      )
  stats::sigma(fm)^2
}
#> [1] 602844.8