Prints approximate least significant differences for REML means (R.W. Payne).

### Options

`PRINT` = string tokens |
Controls printed output (`means` , `sed` , `lsd` , `df` ); default lsd |
---|---|

`FACTORIAL` = scalar |
Limit on the number of factors in each term; default 3 |

`LSDLEVEL` = scalar |
Significance level (%) to use in the calculation of least significant differences; default 5 |

`DFMETHOD` = string token |
Specifies which degrees of freedom to use for the t-statistics (`fddf` , `given` , `tryfddf` ); default `fddf` |

`DFGIVEN` = scalar |
Specifies the number of degrees of freedom to use for the t-statistics when `DFMETHOD=given` , or if d.d.f. are unavailable when `DFMETHOD=tryfddf` |

`FMETHOD` = string token |
Controls how to calculate denominator degrees of freedom for the F-statistics, if these are not already available in the `REML` save structure (`automatic` , `algebraic` , `numerical` ); default `auto` |

`SAVE` = `REML` save structure |
Save structure to provide the table of means; default uses the save structure from the most recent `REML` |

### Parameters

`TERMS` = formula |
Treatment terms whose means are to be compared; default `*` takes the `REML` fixed model |
---|---|

`MEANS` = pointer or table |
Saves the means for each term |

`SED` = pointer or symmetric matrix |
Saves standard errors of differences between means |

`LSD` = pointer or symmetric matrix |
Saves approximate least significant differences matrix for the means |

`DF` = pointer or scalar |
Saves the degrees of freedom used to calculate the t critical values for the LSDs |

`DDF` = pointer or scalar |
Saves the denominator degrees of freedom in the F test for the term |

`DFRANGE` = pointer or scalar |
Saves the range of denominator degrees of freedom in the F tests for the term and any terms that are marginal to the term (available only when denominator degrees of freedom of F-statistics are being used) |

### Description

`VLSD`

calculates least significant differences (LSDs) for predicted means of fixed terms in a `REML`

analysis. These are calculated by multiplying standard errors for differences by the t-statistic that would be used to assess whether those differences are non-zero.

The `TERMS`

parameter specifies a model formula to define the fixed terms whose predicted means are to be compared. The means are usually taken from the most recent analysis performed by `REML`

, but you can set the `SAVE`

option to a save structure from another `REML`

if you want to examine means from an earlier analysis. As in `VCOMPONENTS`

, the `FACTORIAL`

option sets a limit on the number of factors in each term (default 3).

The `DFMETHOD`

option specifies how to obtain the degrees of freedom for the t-statistics. The default is to use the numbers of denominator degrees of freedom printed by `REML`

in the `d.d.f.`

column in the table of tests for fixed tests (produced by setting option `PRINT=wald`

). The degrees of freedom are relevant for assessing the fixed term as a whole, and may vary over the contrasts amongst the means of the term. So the LSDs should be used with caution. (If you are interested in a specific comparison, you should set up a 2-level factor to fit this explicitly in the analysis.) The `FMETHOD`

option controls how the denominator degrees of freedom should be calculated, if they are not already available in the `REML`

save structure (e.g. because they were printed in the original analysis). The settings are the same as in the `REML`

and `VKEEP`

directives, except that there is no `none`

setting. (You would set this option only if you really do want to calculate them.)

In some of the more complicated analyses, `REML`

may be unable to calculate the denominator degrees of freedom. You might then want to supply the number of degrees of freedom yourself, using the `DFGIVEN`

option, rather than having no least significant differences at all. For example, you could use the number of denominator degrees of freedom from the analysis of an earlier similar design. However, the results will only be as good as the degrees of freedom that you have supplied, and thus should be used with caution! You can set option `DFMETHOD=tryfddf`

to use the denominator degrees of freedom, if these can be calculated, or those specified by `DFGIVEN`

otherwise. The setting `DFMETHOD=given`

always uses the degrees of freedom specified by `DFGIVEN`

.

Printed output is controlled by the `PRINT`

option, with settings:

`means` |
prints the means; |
---|---|

`sed` |
prints standard errors for differences between the means; |

`lsd` |
prints least significant differences for the means; |

`df` |
prints the degrees of freedom used to calculate the t critical value required for the LSD, together with the denominator degrees of freedom in the F test for the term if these are not the same. |

The significance level to use in the calculation of the least significant differences can be changed from the default of 5% using the `LSDLEVEL`

option.

The `MEANS`

parameter can save the means. If the `TERMS`

parameter specifies a single term, `MEANS`

must be undeclared or set to a table. If `TERMS`

specifies several terms, you must supply a pointer which will then be set up to contain as many tables as there are terms. Similarly the `SED`

parameter can save the standard errors of differences, the `LSD`

parameter can save the approximate least significant differences, the `DF`

parameter can save the degrees of freedom used to calculate the t-statistics, and the `DDF`

parameter can save the denominator degrees of freedom in the F tests.

When a term involves several factors, its means may be be formed from the effects of several terms. For example, the means for the term `A.B`

will involve the effects for the terms `A`

and `B`

(if these are in the model), as well as those for the term `A.B`

. Different contrasts between the means will then have different denominator degrees of freedom. For caution, if `VLSD`

is using the number of denominator degrees of freedom, it uses the smallest number over the terms that are involved in calculating each table of the means. (This corresponds to the largest t-statistic.) If the difference in the t-statistics calculated from smallest and largest numbers of degrees of freedom differ by more than 1%, `VLSD`

prints a warning message. If the denominator degrees of freedom are being used, their range for each term can be saved by the `DFRANGE`

parameter.

Options: `PRINT`

, `FACTORIAL`

, `LSDLEVEL`

, `DFMETHOD`

, `DFGIVEN`

, `FMETHOD`

, `SAVE`

.

Parameter: `TERMS`

, `MEANS`

, `SED`

, `LSD`

, `DF`

, `DDF`

, `DFRANGE`

.

### See also

Directive: `VDISPLAY`

.

Procedure: `VMCOMPARISON`

.

Commands for: REML analysis of linear mixed models.

### Example

CAPTION 'VLSD example',\ 'Example 5.3.6 from The Guide to Genstat, Part 2 Statistics';\ STYLE=meta,plain FACTOR [NVALUES=322; LEVELS=27] Dam & [NVALUES=322; LEVELS=18] Pup FACTOR [NVALUES=322; LEVELS=2; LABELS=!T('M','F')] Sex FACTOR [NVALUES=322; LEVELS=3; LABELS=!T('C','Low','High')] Dose VARIATE [NVALUES=322] Littersize,Weight READ Dose,Sex,Littersize,Dam,Pup,Weight; FREP=2(labels),4(levels) C M 12 1 1 6.60 C M 12 1 2 7.40 C M 12 1 3 7.15 C M 12 1 4 7.24 C M 12 1 5 7.10 C M 12 1 6 6.04 C M 12 1 7 6.98 C M 12 1 8 7.05 C F 12 1 9 6.95 C F 12 1 10 6.29 C F 12 1 11 6.77 C F 12 1 12 6.57 C M 14 2 1 6.37 C M 14 2 2 6.37 C M 14 2 3 6.90 C M 14 2 4 6.34 C M 14 2 5 6.50 C M 14 2 6 6.10 C M 14 2 7 6.44 C M 14 2 8 6.94 C M 14 2 9 6.41 C F 14 2 10 5.92 C F 14 2 11 6.04 C F 14 2 12 5.82 C F 14 2 13 6.04 C F 14 2 14 5.96 C M 4 3 1 7.50 C M 4 3 2 7.08 C F 4 3 3 7.57 C F 4 3 4 7.27 C M 14 4 1 6.25 C M 14 4 2 6.93 C M 14 4 3 6.80 C M 14 4 4 6.69 C M 14 4 5 6.28 C M 14 4 6 6.27 C M 14 4 7 6.27 C M 14 4 8 6.47 C F 14 4 9 6.29 C F 14 4 10 5.98 C F 14 4 11 6.32 C F 14 4 12 6.28 C F 14 4 13 5.65 C F 14 4 14 5.57 C M 13 5 1 7.96 C M 13 5 2 6.84 C M 13 5 3 7.00 C M 13 5 4 8.10 C M 13 5 5 6.52 C M 13 5 6 7.23 C M 13 5 7 6.10 C M 13 5 8 7.31 C F 13 5 9 7.16 C F 13 5 10 7.09 C F 13 5 11 7.14 C F 13 5 12 5.02 C F 13 5 13 6.04 C M 9 6 1 8.26 C M 9 6 2 7.73 C M 9 6 3 8.33 C M 9 6 4 6.14 C M 9 6 5 7.75 C M 9 6 6 6.96 C F 9 6 7 7.26 C F 9 6 8 6.58 C F 9 6 9 3.68 C M 18 7 1 6.29 C M 18 7 2 6.32 C M 18 7 3 6.28 C M 18 7 4 6.24 C M 18 7 5 6.78 C M 18 7 6 6.63 C M 18 7 7 6.27 C M 18 7 8 6.29 C M 18 7 9 6.06 C F 18 7 10 6.16 C F 18 7 11 5.96 C F 18 7 12 6.26 C F 18 7 13 5.83 C F 18 7 14 6.11 C F 18 7 15 6.45 C F 18 7 16 6.25 C F 18 7 17 6.31 C F 18 7 18 5.74 C M 17 8 1 6.04 C M 17 8 2 5.84 C M 17 8 3 6.77 C M 17 8 4 5.59 C M 17 8 5 5.52 C M 17 8 6 6.42 C M 17 8 7 5.97 C M 17 8 8 6.34 C F 17 8 9 6.23 C F 17 8 10 5.95 C F 17 8 11 6.16 C F 17 8 12 6.19 C F 17 8 13 5.32 C F 17 8 14 5.00 C F 17 8 15 6.30 C F 17 8 16 5.00 C F 17 8 17 5.56 C M 17 9 1 5.37 C M 17 9 2 5.58 C M 17 9 3 5.51 C M 17 9 4 5.19 C M 17 9 5 5.34 C M 17 9 6 5.77 C M 17 9 7 5.17 C M 17 9 8 4.57 C M 17 9 9 5.39 C M 17 9 10 5.62 C M 17 9 11 5.40 C M 17 9 12 5.77 C M 17 9 13 5.24 C F 17 9 14 5.37 C F 17 9 15 5.33 C F 17 9 16 5.44 C F 17 9 17 5.14 C M 13 10 1 7.30 C M 13 10 2 6.60 C M 13 10 3 6.58 C M 13 10 4 6.68 C M 13 10 5 6.46 C M 13 10 6 6.38 C F 13 10 7 6.44 C F 13 10 8 6.67 C F 13 10 9 6.43 C F 13 10 10 6.53 C F 13 10 11 5.92 C F 13 10 12 6.52 C F 13 10 13 6.44 Low M 16 11 1 6.65 Low M 16 11 2 5.78 Low M 16 11 3 6.23 Low M 16 11 4 5.70 Low M 16 11 5 5.73 Low M 16 11 6 6.10 Low M 16 11 7 5.55 Low M 16 11 8 5.71 Low M 16 11 9 5.81 Low M 16 11 10 6.10 Low F 16 11 11 5.54 Low F 16 11 12 5.72 Low F 16 11 13 5.50 Low F 16 11 14 5.64 Low F 16 11 15 5.42 Low F 16 11 16 5.42 Low F 2 12 1 6.89 Low F 2 12 2 7.73 Low M 12 13 1 5.83 Low M 12 13 2 5.97 Low M 12 13 3 6.39 Low M 12 13 4 5.69 Low M 12 13 5 5.69 Low M 12 13 6 5.97 Low M 12 13 7 6.04 Low M 12 13 8 5.46 Low F 12 13 9 6.09 Low F 12 13 10 5.39 Low F 12 13 11 5.89 Low F 12 13 12 5.14 Low M 15 14 1 5.92 Low M 15 14 2 5.75 Low M 15 14 3 6.22 Low M 15 14 4 5.96 Low M 15 14 5 5.59 Low M 15 14 6 5.79 Low M 15 14 7 6.23 Low M 15 14 8 5.88 Low M 15 14 9 6.02 Low F 15 14 10 5.66 Low F 15 14 11 5.76 Low F 15 14 12 5.73 Low F 15 14 13 5.33 Low F 15 14 14 5.58 Low F 15 14 15 5.88 Low M 13 15 1 6.00 Low M 13 15 2 6.11 Low M 13 15 3 6.40 Low M 13 15 4 6.06 Low M 13 15 5 6.39 Low M 13 15 6 6.09 Low M 13 15 7 6.32 Low F 13 15 8 5.96 Low F 13 15 9 6.32 Low F 13 15 10 5.83 Low F 13 15 11 5.97 Low F 13 15 12 5.87 Low F 13 15 13 5.67 Low M 13 16 1 6.43 Low M 13 16 2 6.13 Low M 13 16 3 5.87 Low F 13 16 4 6.09 Low F 13 16 5 5.63 Low F 13 16 6 5.84 Low F 13 16 7 6.20 Low F 13 16 8 6.42 Low F 13 16 9 5.90 Low F 13 16 10 5.62 Low F 13 16 11 6.23 Low F 13 16 12 5.85 Low F 13 16 13 5.89 Low M 14 17 1 5.81 Low M 14 17 2 5.44 Low M 14 17 3 5.65 Low M 14 17 4 5.25 Low M 14 17 5 5.45 Low M 14 17 6 5.32 Low M 14 17 7 5.89 Low F 14 17 8 5.63 Low F 14 17 9 5.12 Low F 14 17 10 5.65 Low F 14 17 11 5.29 Low F 14 17 12 5.13 Low F 14 17 13 5.60 Low F 14 17 14 5.08 Low M 15 18 1 6.77 Low M 15 18 2 7.13 Low M 15 18 3 6.85 Low F 15 18 4 6.49 Low F 15 18 5 6.09 Low F 15 18 6 6.09 Low F 15 18 7 5.99 Low F 15 18 8 6.01 Low F 15 18 9 6.11 Low F 15 18 10 6.15 Low F 15 18 11 4.75 Low F 15 18 12 5.69 Low F 15 18 13 6.19 Low F 15 18 14 5.72 Low F 15 18 15 6.14 Low M 10 19 1 6.72 Low M 10 19 2 6.34 Low M 10 19 3 6.48 Low M 10 19 4 5.74 Low F 10 19 5 6.11 Low F 10 19 6 5.71 Low F 10 19 7 6.41 Low F 10 19 8 6.21 Low F 10 19 9 6.11 Low F 10 19 10 5.81 Low M 16 20 1 5.90 Low M 16 20 2 6.22 Low M 16 20 3 6.67 Low M 16 20 4 6.23 Low M 16 20 5 6.24 Low M 16 20 6 6.26 Low M 16 20 7 6.38 Low M 16 20 8 6.05 Low M 16 20 9 5.89 Low M 16 20 10 6.29 Low F 16 20 11 6.12 Low F 16 20 12 5.40 Low F 16 20 13 5.50 Low F 16 20 14 5.46 Low F 16 20 15 5.97 Low F 16 20 16 6.11 High M 14 21 1 5.09 High M 14 21 2 5.57 High M 14 21 3 5.69 High M 14 21 4 5.50 High M 14 21 5 5.45 High M 14 21 6 5.24 High M 14 21 7 5.36 High M 14 21 8 5.26 High M 14 21 9 5.36 High M 14 21 10 5.01 High M 14 21 11 5.03 High F 14 21 12 5.23 High F 14 21 13 5.13 High F 14 21 14 4.48 High M 10 22 1 5.30 High M 10 22 2 5.40 High M 10 22 3 5.55 High M 10 22 4 6.02 High M 10 22 5 5.27 High F 10 22 6 5.19 High F 10 22 7 5.42 High F 10 22 8 5.40 High F 10 22 9 5.12 High F 10 22 10 5.40 High M 3 23 1 7.70 High F 3 23 2 7.68 High F 3 23 3 6.33 High M 12 24 1 6.28 High M 12 24 2 5.74 High M 12 24 3 6.29 High F 12 24 4 5.68 High F 12 24 5 5.76 High F 12 24 6 6.03 High F 12 24 7 5.30 High F 12 24 8 5.55 High F 12 24 9 6.53 High F 12 24 10 5.76 High F 12 24 11 5.77 High F 12 24 12 5.49 High M 8 25 1 6.50 High M 8 25 2 7.10 High M 8 25 3 7.00 High M 8 25 4 7.00 High M 8 25 5 5.85 High F 8 25 6 6.10 High F 8 25 7 6.63 High F 8 25 8 6.33 High M 9 26 1 7.00 High M 9 26 2 6.15 High F 9 26 3 6.22 High F 9 26 4 6.20 High F 9 26 5 5.76 High F 9 26 6 6.21 High F 9 26 7 6.42 High F 9 26 8 6.42 High F 9 26 9 6.30 High M 9 27 1 5.64 High M 9 27 2 6.06 High M 9 27 3 6.56 High M 9 27 4 6.29 High M 9 27 5 5.69 High M 9 27 6 6.36 High F 9 27 7 5.93 High F 9 27 8 5.74 High F 9 27 9 5.74 : VCOMPONENTS [FIXED=Littersize+Dose*Sex] RANDOM=Dam/Pup REML [PRINT=model,components,wald] Weight VLSD [PRINT=means,lsd] Dose*Sex