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One-way analysis of variance of genotypes conducted in both randomized complete block and alpha-lattice designs.
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.- 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 functiongamem()to analyze a one-way trial with mixed-effect models.- by
One variable (factor) to compute the function by. It is a shortcut to
dplyr::group_by().This is especially useful, for example, when the researcher want to fit a fixed-effect model for each environment. In this case, an object of class gafem_grouped is returned.mgidi()can then be used to compute the mgidi index within each environment.- prob
The error probability. Defaults to 0.05.
- verbose
Logical argument. If
verbose = FALSEthe 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
fittedcolumn, residuals in theresidcolumn, standardized residuals in thestdrescolumn, the diagonal of the 'hat' matrix in thehat, and standard errors for the fitted values in these.fitcolumn.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);Maxthe maximum observed,MinGENthe 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.
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))
#> Evaluating trait PH |========= | 20% 00:00:00
Evaluating trait ED |================== | 40% 00:00:00
Evaluating trait EL |========================== | 60% 00:00:00
Evaluating trait CL |=================================== | 80% 00:00:01
Evaluating trait CW |============================================| 100% 00:00:01
#> ---------------------------------------------------------------------------
#> One-way ANOVA table (Randomized complete block design)
#> ---------------------------------------------------------------------------
#> model PH ED EL CL CW
#> REP 0.2328 1.40e-01 0.532 9.45e-03 4.10e-02
#> GEN 0.0239 1.38e-05 0.373 1.18e-06 6.34e-06
#> Residuals NA NA NA NA NA
#> ---------------------------------------------------------------------------
#> Variables with nonsignificant genotype effect
#> EL
#> ---------------------------------------------------------------------------
#>
# Fitted values
get_model_data(rcbd)
#> Class of the model: gafem
#> Variable extracted: fitted
#> # A tibble: 39 × 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)
#> Evaluating trait YIELD |=========================================| 100% 00:00:00
#> ---------------------------------------------------------------------------
#> One-way ANOVA table (Alpha-lattice design)
#> ---------------------------------------------------------------------------
#> model YIELD
#> REP 6.59e-09
#> GEN 3.63e-07
#> BLOCK(REP) 6.25e-03
#> Residuals NA
# Fitted values
get_model_data(alpha)
#> Class of the model: gafem
#> Variable extracted: fitted
#> # A tibble: 72 × 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
# }