One-way analysis of variance of genotypes conducted in both randomized complete block and alpha-lattice designs.

gafem(.data, gen, rep, resp, prob = 0.05, block = NULL, verbose = TRUE)

Arguments

.data

The dataset containing the columns related to, Genotypes, replication/block and response variable(s).

gen

The name of the column that contains the levels of the genotypes, that will be treated as random effect.

rep

The name of the column that contains the levels of the replications (assumed to be fixed).

resp

The response variable(s). To analyze multiple variables in a single procedure a vector of variables may be used. For example resp = c(var1, var2, var3). Select helpers are also allowed.

prob

The error probability. Defaults to 0.05.

block

Defaults to NULL. In this case, a randomized complete block design is considered. If block is informed, then a resolvable alpha-lattice design (Patterson and Williams, 1976) is employed. All effects, except the error, are assumed to be fixed. Use the function gamem to analyze a one-way trial with mixed-effect models.

verbose

Logical argument. If verbose = FALSE the code are run silently.

Value

A list where each element is the result for one variable containing the following objects:

  • anova: The one-way ANOVA table.

  • model: The model with of lm.

  • augment: Information about each observation in the dataset. This includes predicted values in the fitted column, residuals in the resid column, standardized residuals in the stdres column, the diagonal of the 'hat' matrix in the hat, and standard errors for the fitted values in the se.fit column.

  • hsd: The Tukey's 'Honest Significant Difference' for genotype effect.

  • details: A tibble with the following data: Ngen, the number of genotypes; OVmean, the grand mean; Min, the minimum observed (returning the genotype and replication/block); Max the maximum observed, MinGEN the loser winner genotype, MaxGEN, the winner genotype.

Details

gafem analyses data from a one-way genotype testing experiment. By default, a randomized complete block design is used according to the following model: \[Y_{ij} = m + g_i + r_j + e_{ij}\] where \(Y_{ij}\) is the response variable of the ith genotype in the jth block; m is the grand mean (fixed); \(g_i\) is the effect of the ith genotype; \(r_j\) is the effect of the jth replicate; and \(e_{ij}\) is the random error.

When block is informed, then a resolvable alpha design is implemented, according to the following model:

\[Y_{ijk} = m + g_i + r_j + b_{jk} + e_{ijk}\] where where \(y_{ijk}\) is the response variable of the ith genotype in the kth block of the jth replicate; m is the intercept, \(t_i\) is the effect for the ith genotype \(r_j\) is the effect of the jth replicate, \(b_{jk}\) is the effect of the kth incomplete block of the jth replicate, and \(e_{ijk}\) is the plot error effect corresponding to \(y_{ijk}\). All effects, except the random error are assumed to be fixed.

References

Patterson, H.D., and E.R. Williams. 1976. A new class of resolvable incomplete block designs. Biometrika 63:83-92.

See also

Author

Tiago Olivoto tiagoolivoto@gmail.com

Examples

# \donttest{ library(metan) # RCBD rcbd <- gafem(data_g, gen = GEN, rep = REP, resp = c(PH, ED, EL, CL, CW))
#> variable PH #> --------------------------------------------------------------------------- #> One-way ANOVA table (randomized complete block design) #> --------------------------------------------------------------------------- #> Source Df Sum Sq Mean Sq F value Pr(>F) #> REP 2 0.101 0.0507 1.55 0.2328 #> GEN 12 1.008 0.0840 2.56 0.0239 #> Residuals 24 0.786 0.0328 NA NA #> --------------------------------------------------------------------------- #> #> variable ED #> --------------------------------------------------------------------------- #> One-way ANOVA table (randomized complete block design) #> --------------------------------------------------------------------------- #> Source Df Sum Sq Mean Sq F value Pr(>F) #> REP 2 10.4 5.19 2.13 1.40e-01 #> GEN 12 222.4 18.54 7.63 1.38e-05 #> Residuals 24 58.3 2.43 NA NA #> --------------------------------------------------------------------------- #> #> variable EL #> --------------------------------------------------------------------------- #> One-way ANOVA table (randomized complete block design) #> --------------------------------------------------------------------------- #> Source Df Sum Sq Mean Sq F value Pr(>F) #> REP 2 1.27 0.637 0.648 0.532 #> GEN 12 13.51 1.126 1.144 0.373 #> Residuals 24 23.61 0.984 NA NA #> --------------------------------------------------------------------------- #> #> variable CL #> --------------------------------------------------------------------------- #> One-way ANOVA table (randomized complete block design) #> --------------------------------------------------------------------------- #> Source Df Sum Sq Mean Sq F value Pr(>F) #> REP 2 16.1 8.06 5.7 9.45e-03 #> GEN 12 170.7 14.22 10.1 1.18e-06 #> Residuals 24 34.0 1.41 NA NA #> --------------------------------------------------------------------------- #> #> variable CW #> --------------------------------------------------------------------------- #> One-way ANOVA table (randomized complete block design) #> --------------------------------------------------------------------------- #> Source Df Sum Sq Mean Sq F value Pr(>F) #> REP 2 55.2 27.59 3.66 4.10e-02 #> GEN 12 755.0 62.92 8.34 6.34e-06 #> Residuals 24 181.0 7.54 NA NA #> --------------------------------------------------------------------------- #> #> --------------------------------------------------------------------------- #> Variables with nonsignificant genotype effect #> EL #> --------------------------------------------------------------------------- #> Done!
# Fitted values get_model_data(rcbd)
#> Class of the model: gafem
#> Variable extracted: fitted
#> # A tibble: 39 x 8 #> GEN REP factors PH ED EL CL CW #> <fct> <fct> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> #> 1 H1 1 H1_1 2.13 50.8 15.1 31.7 27.6 #> 2 H1 2 H1_2 2.21 49.9 14.7 30.1 25.2 #> 3 H1 3 H1_3 2.25 51.1 14.7 30.9 27.8 #> 4 H10 1 H10_1 1.97 44.1 14.2 25.6 13.0 #> 5 H10 2 H10_2 2.05 43.2 13.8 24.0 10.6 #> 6 H10 3 H10_3 2.09 44.4 13.9 24.7 13.2 #> 7 H11 1 H11_1 2.03 47.3 14.5 27.2 16.7 #> 8 H11 2 H11_2 2.11 46.3 14.1 25.6 14.3 #> 9 H11 3 H11_3 2.16 47.5 14.2 26.3 16.9 #> 10 H12 1 H12_1 2.36 48.0 14.2 26.6 18.5 #> # ... with 29 more rows
# ALPHA-LATTICE DESIGN alpha <- gafem(data_alpha, gen = GEN, rep = REP, block = BLOCK, resp = YIELD)
#> variable YIELD #> --------------------------------------------------------------------------- #> One-way ANOVA table (alpha-lattice design) #> --------------------------------------------------------------------------- #> Source Df Sum Sq Mean Sq F value Pr(>F) #> REP 2 6.14 3.0677 36.76 6.59e-09 #> GEN 23 14.08 0.6120 7.33 3.63e-07 #> BLOCK(REP) 15 3.60 0.2402 2.88 6.25e-03 #> Residuals 31 2.59 0.0835 NA NA #> --------------------------------------------------------------------------- #> #> Done!
# Fitted values get_model_data(alpha)
#> Class of the model: gafem
#> Variable extracted: fitted
#> # A tibble: 72 x 5 #> GEN REP BLOCK factors YIELD #> <fct> <fct> <fct> <chr> <dbl> #> 1 G11 R1 B1 G11_R1_B1 4.41 #> 2 G04 R1 B1 G04_R1_B1 4.73 #> 3 G05 R1 B1 G05_R1_B1 5.23 #> 4 G22 R1 B1 G22_R1_B1 4.65 #> 5 G21 R1 B2 G21_R1_B2 4.61 #> 6 G10 R1 B2 G10_R1_B2 4.21 #> 7 G20 R1 B2 G20_R1_B2 4.04 #> 8 G02 R1 B2 G02_R1_B2 4.32 #> 9 G23 R1 B3 G23_R1_B3 4.11 #> 10 G14 R1 B3 G14_R1_B3 4.70 #> # ... with 62 more rows
# }