---
title: "Simulation and planning the number of replicates"
author: "Muhammad Yaseen"
date: last-modified
format:
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vignette: >
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execute:
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{{< 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

Simulated data with known effects show how well an analysis recovers them, which is useful in teaching, and how
often its tests detect effects of a given size, which is the basis for planning an experiment. `DiallelSim()` draws
the data and `DiallelPower()` estimates the power of the combining-ability tests.

# Simulation and the number of replicates

`DiallelSim()` draws plot data from Griffing's model with chosen standard deviations of the effects and returns the
true effects with the data, so the estimates can be compared with the truth:

```{r sim}
s <-
  DiallelSim(
      Parents = 6
    , Method  = 1
    , Rep     = 4
    , Env     = 1
    , Mean    = 100
    , gca     = 5
    , sca     = 3
    , rec     = 1
    , gcaEnv  = 0
    , scaEnv  = 0
    , EnvSD   = 0
    , Block   = 2
    , Error   = 4
    , seed    = 123
    )
fs <-
  Griffing(
      y          = y
    , Rep        = Rep
    , Cross1     = Cross1
    , Cross2     = Cross2
    , data       = s
    , Method     = 1
    , Model      = 1
    , Reciprocal = c("combined", "split")[1]
    )
round(x = cbind(true = attr(x = s, which = "truth")$gca, estimated = fs$GCA), digits = 2)
```

`DiallelPower()` repeats such simulations to estimate the power of the gca and sca tests for several numbers of
replicates, which helps to plan an experiment:

```{r power}
pw <-
  DiallelPower(
      Parents = 6
    , Method  = 2
    , Rep     = 2:5
    , Model   = 1
    , gca     = 1
    , sca     = 1.5
    , rec     = 0
    , Error   = 4
    , nsim    = 200
    , alpha   = 0.05
    , seed    = 1
    )
pw
plot(x = pw)
```

# Summary

`DiallelSim()` gives data with known effects for teaching and checking; `DiallelPower()` shows how many replicates
detect gca and sca effects of a given size.

# 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.