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