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VAIC procedure

Calculates the Akaike and Schwarz (Bayesian) information coefficients for REML (R.W. Payne).

Options

PRINT = string tokens Controls printed output (deviance, aic, bic, sic, dffixed, dfrandom, changes); default aic
INCLUDE = string tokens Which constants to include that depend only on the fixed model (determinant, pi); default pi
DMETHOD = string token Method to use to calculate log(determinant(X′X)) (choleski, lrv); default chol
REPEAT = string token Whether to repeat output from the previous VAIC (yes, no); default no

Parameters

DEVIANCE = scalars Saves the deviance
AIC = scalars Saves the Akaike information coefficient
SIC = scalars Saves the Schwarz (Bayesian) information coefficient
DFFIXED = scalars Saves the number of parameters fitted in the fixed model
DFRANDOM = scalars saves the number of parameters fitted in the random model (and any covariance models)
CHANGES = variates Saves changes since the previous VAIC; the units of the variates are labelled by the names of the coefficients (deviance, aic, sic, dffixed and dfrandom)
SAVE = REML save structures Save structure for which to calculate the coefficients; default uses the save structure from the most recent REML

Description

The Akaike and Schwarz (Bayesian) information coefficients are often used to assess the appropriateness of random (and covariance) models in REML. They are calculated from the deviance (which can be printed by REML):

aic = deviance + 2 × r

sic = deviance + log(np) × r

where n is the total number of usable units in the analysis, r is the number of parameters fitted in the random model (and any covariance models), and p is the number of parameters fitted in the fixed model.

An additional consideration is that the deviance provided by REML omits some constants that depend on the fixed model. In fact the full deviance is given by

full-deviance = REML-deviance + (np)*log(2π) – log(det(X′X))

where X is the design matrix of the fixed model. Other software systems tend to include the first term, involving π, but omit the log-determinant term which is more time-consuming to calculate. The inclusion of these terms in the calculation is controlled by the INCLUDE option, with settings

    determinant -log(det(X′X))
    pi +(n-p)*log(2π)

The DMETHOD option controls how -log(det(X′X)) is calculated when this is included. However, the default is INCLUDE=pi.

Printed output is controlled by the PRINT option, with settings:

    deviance prints the deviance (adding the extra terms specified by INCLUDE);
    aic prints the Akaike information coefficient;
    bic or sic (synonyms) print the Schwarz (Bayesian) information coefficient;
    dffixed prints the number of parameters fitted in the fixed model;
    dfrandom prints the number of parameters fitted in the random model (and any covariance models);
    changes prints changes in the values of the coefficients since the previous use of VAIC, provided the fixed model of the REML analysis has not also changed.

These can all be saved using the DEVIANCE, AIC, SIC, DFFIXED, DFRANDOM and CHANGES parameters. By default VAIC prints just the Akaike information coefficient.

By default, each time that you use VAIC, its record of the current and previous REML analyses is updated. However, you can set option REPEAT=yes to repeat output from the previous VAIC. The analysis record is then not updated, so the information required to calculate changes remains available.

The coefficients are usually calculated for the most recent REML analysis. However, you can use the SAVE parameter to specify the save structure from an earlier analysis.

Options: PRINT, INCLUDE, DMETHOD, REPEAT.

Parameters: DEVIANCE, AIC, SIC, DFFIXED, DFRANDOM, CHANGES, SAVE.

See also

Procedure: VRACCUMULATE.

Commands for: REML analysis of linear mixed models.

Example

CAPTION     'VAIC 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
VAIC
Updated on March 4, 2019

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