Display residuals in field layout (R.W. Payne & A.D.Todd).

### Options

`PRINT` = string tokens |
Controls output (`contour` , `shade` , `table` ); default `cont` |
---|---|

`GRAPHICS` = string token |
Type of graph (`highresolution` , `lineprinter` ); default `high` |

`METHOD` = string token |
Type of residuals to take from the save structure when the `RESIDUALS` parameter is not specified (`combined` , `finalstratum` , `standardizedfinal` ); default `comb` |

`MARGIN` = string token |
Whether to include margins in printed tables (`yes` , `no` ); default `no` |

`YORIENTATION` = string token |
Y-axis orientation of the plot (reverse, normal); default `norm` |

`PENCONTOUR` = scalar |
Pen number to be used for the contours; default 1 |

`PENFILL` = scalar or variate |
Pen number(s) defining how to fill the areas between contours; default 3 |

`PENSHADE` = scalar or variate |
Pen(s) to use for the shade plot; default 3 |

### Parameters

`Y` = variates or factors |
Specifies the y-coordinates of the plots |
---|---|

`X` = variates or factors |
Specifies the x-coordinates of the plots |

`RESIDUALS` = variates |
Residuals to be plotted; default is to take the residuals from the save structure specified by the `SAVE` option, or from the most recent `ANOVA` if that is unspecified |

`SAVE` = `ANOVA` , `REML` or regression save structures |
Save structure of the `ANOVA` , `REML` or regression analysis from which to take the residuals if the `RESIDUALS` parameter is not specified; default is to take the most recent `ANOVA` analysis |

`FIELDWIDTH` = scalars |
Field width for printing the residuals; default 12 |

`DECIMALS` = scalars |
Number of decimal places to use when printing the residuals |

`TITLE` = texts |
Titles for the plots |

### Description

In a field experiment it can be useful to study the spatial pattern of the residuals, for example to see if there are any systematic trends in fertility.

The locations of the plots are defined by the `Y`

and `X`

parameters, specifying variates or factors containing their y- and x-coordinates respectively. The residuals can be supplied, in a variate, by the `RESIDUALS`

parameter. If this is not set, the default is to take the residuals from the most recent `ANOVA`

analysis. You can take the residuals from some other analysis, by specifying its save structure using the `SAVE`

parameter. This can be from another `ANOVA`

analysis, a `REML`

analysis or a regression analysis (see `MODEL`

).

The `METHOD`

option determines the type of residuals that are taken. The default setting `combined`

gives residuals combining the residuals from all the strata or error terms in the analysis. These corresponds to the `CBRESIDUALS`

option of the `AKEEP`

directive, or the use of the `RESIDUALS`

option in `VKEEP`

with option `RMETHOD=all`

. Regression allows only a single error term, so `combined`

is treated as the same as the next setting, `finalstratum`

.

The setting `finalstratum`

uses simple residuals from the final stratum or error term. These correspond to the `RESIDUALS`

option of `AKEEP`

with option `RMETHOD=simple`

, or the `RESIDUALS`

option of `VKEEP`

with option `RMETHOD=final`

, or the `RESIDUALS`

parameter of `RKEEP`

with option `RMETHOD=simple`

.

The last setting, `standardizedfinal`

, uses standardized residuals from the final stratum or error term. These correspond to the `RESIDUALS`

option of `AKEEP`

with option `RMETHOD=standardized`

, or the `RESIDUALS`

parameter of `RKEEP`

with option `RMETHOD=deviance`

. They are calculated using standard errors from procedure `VFRESIDUALS`

for `REML`

analyses.

Usually, the plots will all have different coordinates. However, if there are several plots with the same coordinates, mean residuals are calculated for each location. Thus for example, if you wanted only to look at the block and whole-plot residuals in a split-plot design, you could request combined residuals and then set identical coordinates for the (sub-) plots within each whole plot.

`AFIELDRESIDUALS`

provides three forms of representation, selected using the `PRINT`

option as follows:

`table` |
prints the residuals in a table whose structure corresponds to the field layout, |
---|---|

`contour` |
generates a contour plot if the plots are on a regular grid or a line graph if they are arranged in a single line, and |

`shade` |
can produce a shade plot for plots that are on a regular grid. |

The `GRAPHICS`

option determines the type of graphics that is used, with settings `highresolution`

(the default) and `lineprinter`

. No graph can be produced if the plots are in an irregular 2-dimensional arrangement. High-resolution contour plots require more than 3 rows and columns, and line-printer contour plots require more than 4 rows and columns. The way in which the lines are drawn in high-resolution contour plots is defined by the properties of the pen specified by the `PENCONTOUR`

option, while the pen specified by the `PENFILL`

parameter defines how to shade the areas between the contours. Their defaults are 1 and 3 respectively. Similarly, the pen or pens specified by the `PENSHADE`

option control the colouring of the shade plot; the default is to use pen 3. For more information see the `DCONTOUR`

and `DSHADE`

directives.

The `MARGIN`

option, with settings `no`

(default) and `yes`

, determines whether or not marginal summaries are included with the printed tables. The `FIELDWIDTH`

and `DECIMALS`

parameters can be used to specify the formats of the printed tables (as in the `PRINT`

directive). The `TITLE`

parameter can supply a title for the plots. If this is unset, a default title is formed.

The `YORIENTATION`

option controls the orientation of the y-coordinates in the plots and tables. By default this is `normal`

, so that they run upwards from the bottom of the page (as in a map).

Options: `PRINT`

, `GRAPHICS`

, `METHOD`

, `MARGIN`

, `YORIENTATION`

, `PENCONTOUR`

, `PENFILL`

, `PENSHADE`

.

Parameters: `Y`

, `X`

, `RESIDUALS`

, `SAVE`

, `FIELDWIDTH`

, `DECIMALS`

, `TITLE`

.

### Method

`AFIELDRESIDUALS`

obtains the residuals using the `AKEEP`

, `VKEEP`

or `RKEEP`

directives, and then uses the standard Genstat facilities for manipulation and plotting.

### Action with `RESTRICT`

If any of `X`

, `Y`

or `RESIDUALS`

is restricted, only the unrestricted plots are displayed.

### See also

Directive: `ANOVA`

.

Procedures: `AGRAPH`

, `APLOT`

, `VDFIELDRESIDUALS`

.

Commands for: Analysis of variance.

### Example

CAPTION 'AFIELDRESIDUALS example',!t(\ 'Split plot design (Yates,F: The Design and Analysis of Factorial',\ 'Experiments Commonwealth Bureau of Soils, Tech. Comm. 35 p.74)');\ STYLE=meta,plain FACTOR [NVALUES=72; LEVELS=6] Block & [LEVELS=3] Wplot & [LEVELS=4] Subplot GENERATE Block,Wplot,Subplot FACTOR [NVAL=72; LABELS=!T('0 cwt','0.2 cwt','0.4 cwt','0.6 cwt')] Nitrogen & [NVAL=72; LABELS=!T(Victory,'Golden rain',Marvellous)] Variety READ [SERIAL=yes] Nitrogen,Variety,Yield 4 3 2 1 1 2 4 3 1 2 3 4 3 1 2 4 4 1 2 3 2 1 3 4 2 3 4 1 4 2 3 1 1 4 2 3 3 4 1 2 1 3 4 2 2 3 4 1 4 1 3 2 3 4 1 2 3 4 2 1 3 1 4 2 4 3 1 2 1 2 3 4 : 3 3 3 3 1 1 1 1 2 2 2 2 3 3 3 3 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 1 1 1 1 3 3 3 3 2 2 2 2 1 1 1 1 2 2 2 2 1 1 1 1 3 3 3 3 1 1 1 1 2 2 2 2 3 3 3 3 : 156 118 140 105 111 130 174 157 117 114 161 141 104 70 89 117 122 74 89 81 103 64 132 133 108 126 149 70 144 124 121 96 61 100 91 97 109 99 63 70 80 94 126 82 90 100 116 62 96 60 89 102 112 86 68 64 132 124 129 89 118 53 113 74 104 86 89 82 97 99 119 121 : BLOCKSTRUCTURE Block/Wplot/Subplot TREATMENTSTRUCTURE Variety*Nitrogen ANOVA [PRINT=aov,means,residuals; FPROBABILITY=yes] Yield VARIATE X,Y; VALUES=!((1,2)18,(3,4)18),!((2(18...1))2) AFIELDRESIDUALS [PRINT=contour,shade,table] Y=Y; X=X & [METHOD=final] Y=Y; X=X & [METHOD=standardizedfinal] Y=Y; X=X