---
title: "Choosing an analysis"
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{Choosing an analysis}
  %\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

Which function, method and model to use depends on the crosses grown and on the question asked. This vignette gives
a decision table and shows how to check that a data set has the crosses an analysis needs.

# Decision table

| Crosses grown | Question | Function |
|---|---|---|
| parents, $F_1$ and reciprocals | combining ability, reciprocal effects | `Griffing(Method = 1)` |
| parents and one set of $F_1$ | combining ability | `Griffing(Method = 2)` |
| $F_1$ and reciprocals, no parents | combining ability, reciprocal effects | `Griffing(Method = 3)` |
| one set of $F_1$ only | combining ability | `Griffing(Method = 4)` |
| parents, $F_1$ and reciprocals | gene action: additive and dominance components, $W_r$-$V_r$ graph | `Hayman()` |
| parents, $F_1$ and reciprocals | maternal and non-maternal reciprocal effects | `Griffing(Method = 1, Reciprocal = "split")` |
| a published table of cross means | combining ability from the means and the published error | `GriffingMeans()` |
| any of Griffing's layouts in several environments | stability of gca and sca: interactions with environments | `GriffingEnv()` |
| parents and crosses (a check variety optional) | heterosis over the mid-parent, better parent, check | `Heterosis()` |
| parents and one set of $F_1$ | variety effects and average, variety and specific heterosis | `GardnerEberhart()` |
| two groups of parents crossed with each other | combining ability of each group | `PartialDiallel()` |
| lines crossed with testers | combining ability, contributions of lines and testers | `LineTester()` |
| North Carolina Design I, II or III | additive and dominance variance | `NCDesign()` |
| not yet grown | number of replicates for the tests | `DiallelPower()`, `DiallelSim()` |

**Model.** Choose Model 1 (fixed effects) when the parents are of interest in themselves (the usual case in a
breeding programme): it gives effects and standard errors. Choose Model 2 (random effects) when the parents are a
random sample of a population and the aim is to estimate variance components (additive and dominance variance).

# Which method does a data set fit?

```{r cells}
cells <- function(d) {
  i <- as.numeric(as.character(d$Cross1))
  j <- as.numeric(as.character(d$Cross2))
  u <- unique(data.frame(i = i, j = j))
  c(parents = length(unique(c(i, j))), selfs = sum(u$i == u$j), above = sum(u$i < u$j), below = sum(u$i > u$j))
}
rbind(
    Data1 = cells(d = GriffingData1)
  , Data2 = cells(d = GriffingData2)
  , Data3 = cells(d = GriffingData3)
  , Data4 = cells(d = GriffingData4)
  )
```

With $P$ parents: Method 1 needs $P$ selfs and $P(P-1)$ crosses, Method 2 $P$ selfs and $P(P-1)/2$ crosses (either
way round), Method 3 $P(P-1)$ crosses and no selfs, Method 4 $P(P-1)/2$ crosses and no selfs.

# What happens when a plot or a cross is missing

A missing plot is allowed in `Griffing()`, `GriffingEnv()`, `Heterosis()`, `GardnerEberhart()`, `LineTester()` and
`NCDesign()`: the cross means are then least-squares means adjusted for blocks, the number of replicates is the
harmonic mean of the plot numbers, and the label of the result says so. `Hayman()` and `PartialDiallel()` need every
plot. Every cross of the method
must be present, though; a missing cross is reported with its name:

```{r missing}
d <- subset(x = GriffingData1, subset = !(Cross1 == 1 & Cross2 == 2))
tryCatch(
    expr  = Griffing(
        y          = Yield
      , Rep        = Rep
      , Cross1     = Cross1
      , Cross2     = Cross2
      , data       = d
      , Method     = 1
      , Model      = 1
      , Reciprocal = c("combined", "split")[1]
      )
  , error = function(e) conditionMessage(e)
  )
```

Incomplete diallels need a linear mixed model with the gca, sca and reciprocal effects as random terms.

# Column names

The arguments take a column by name, as a string, or a vector:

```{r columns}
d <- GriffingData1
names(d) <- c("Female", "Male", "Block", "GrainYield")
fit <-
  Griffing(
      y          = "GrainYield"
    , Rep        = Block
    , Cross1     = Female
    , Cross2     = Male
    , data       = d
    , Method     = 1
    , Model      = 1
    , Reciprocal = c("combined", "split")[1]
    )
fit$ANOVA
```

# Summary

The crosses grown fix the analysis and the method; the purpose fixes the model. Check the cells before the analysis; every analysis
reports what is missing.

# 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.

Hayman, B. I. (1954). The theory and analysis of diallel crosses. *Genetics*, 39(6), 789--809.

Hayman, B. I. (1954). The analysis of variance of diallel tables. *Biometrics*, 10(2), 235--244.