---
title: "Getting started with DiallelAnalysisR"
author: "Muhammad Yaseen"
date: last-modified
format:
  html:
    self-contained: true
    number-sections: true
    toc: true
    toc-depth: 3
    highlight-style: pygments
    code-tools: true
    html-math-method: mathjax
vignette: >
  %\VignetteIndexEntry{Getting started with DiallelAnalysisR}
  %\VignetteEngine{quarto::html}
  %\VignetteEncoding{UTF-8}
execute:
  echo: true
  warning: false
  message: false
---

{{< include _DiallelAnalysisR-macros.txt >}}

```{r setup, include = FALSE}
knitr::opts_chunk$set(collapse = FALSE, comment = "", fig.width = 7, fig.height = 4.2,
                      dev = if (knitr::is_latex_output()) "cairo_pdf" else
                        if (requireNamespace("svglite", quietly = TRUE)) "svglite" else "png")
if (requireNamespace("DiallelAnalysisR", quietly = TRUE)) library(DiallelAnalysisR) else
  pkgload::load_all(export_all = FALSE, helpers = FALSE, quiet = TRUE)
```

# Abstract

DiallelAnalysisR analyses diallel crosses laid out in randomized complete blocks. This vignette takes one data set,
an eight-parent diallel with reciprocals, from the plot data to the analysis of variance, the combining-ability
effects with their standard errors and the plots, in a few minutes of reading. Each later vignette takes one part
further.

# The data

Each row is one plot: the female parent (`Cross1`), the male parent (`Cross2`), the replicate (`Rep`) and the yield.

```{r data}
head(GriffingData1)
dim(GriffingData1)
with(data = GriffingData1, expr = table(Cross1, Cross2))[1:4, 1:4]
```

The 8 parents, their 28 crosses and the 28 reciprocal crosses (64 cells) are each grown in 4 replicates.

# One analysis

Griffing's Method 1 (parents, $F_1$ and reciprocals) with the fixed-effects model (Model 1):

```{r analysis}
fit <-
  Griffing(
      y          = Yield
    , Rep        = Rep
    , Cross1     = Cross1
    , Cross2     = Cross2
    , data       = GriffingData1
    , Method     = 1
    , Model      = 1
    , Reciprocal = c("combined", "split")[1]
    )
fit
```

The result is the list that `Griffing()` has always returned, with a class that gives it methods:

```{r summary}
summary(fit)
```

# The analysis of variance

```{r anova}
knitr::kable(x = fit$ANOVA, digits = 3)
```

General and specific combining ability are both highly significant; the reciprocal differences are not. The mean
squares are on the scale of a cell mean, so the error line is $MS_E/B$, the residual mean square of the block
analysis divided by the number of replicates.

# Effects and standard errors

```{r effects}
round(x = fit$GCA, digits = 3)
round(x = fit$StdErr, digits = 3)
```

Parents 3 and 7 are the best general combiners, parent 8 the poorest. A difference between two gca effects larger
than about twice `gi_gj` is significant at about the 5% level.

# Plots

```{r plot-gca}
plot(fit)
```

```{r plot-sca, fig.height = 5}
plot(fit, which = "sca")
```

# The usual model functions

`summary()` adds the $t$ tests of every gca effect and the crosses with the largest sca effects; `anova()`, `coef()`,
`vcov()`, `confint()`, `fitted()`, `residuals()` and `predict()` work as for other models in R.

```{r model-functions}
summary(object = fit, top = 5)
head(confint(object = fit, parm = NULL, level = 0.95), 8)
predict(
    object  = fit
  , newdata = data.frame(Cross1 = c(3, 3), Cross2 = c(7, 8))
  , type    = c("gca", "full")[1]
  )
```

The residuals of the block analysis check its assumptions:

```{r residuals}
plot(x = fit, which = c("gca", "sca", "residuals", "qq")[3])
plot(x = fit, which = c("gca", "sca", "residuals", "qq")[4])
```

# Tables for a report

Any component converts to a table, with the row names in a column `term`:

```{r table}
data.table::as.data.table(fit, component = "ANOVA")
```

# Summary

One call of `Griffing()` gives the analysis of variance, the effects with their standard errors and the variance
components; `plot()` draws the effects. Vignette 02 helps choose an analysis; vignettes 04 to 07 explain Griffing's,
Hayman's and the partial diallel analyses, 08 to 11 heterosis, related designs, environments and planning, and 12 the
tables for papers and the interactive application. Vignettes 13 to 15 cover validation, speed and extending the
package.

# References

Griffing, B. (1956). Concept of general and specific combining ability in relation to diallel crossing systems.
*Australian Journal of Biological Sciences*, 9(4), 463--493.

Singh, R. K. and Chaudhary, B. D. (2004). *Biometrical Methods in Quantitative Genetic Analysis*. Kalyani Publishers,
New Delhi.