Fits regressions with an AR1 or a power-distance correlation model (R.W. Payne).
Options
PRINT = string tokens |
What to print (model , deviance , summary , estimates , correlations , fittedvalues , accumulated , monitoring , cparameter , cmonitoring , cplot ); default mode , summ , esti , cpar |
---|---|
CALCULATION = expression structures |
Calculation of explanatory variates involving nonlinear parameters |
CONSTANT = string token |
How to treat the constant (estimate , omit ); default esti |
FACTORIAL = scalars |
Limit for expansion of model terms; default 3 |
POOL = string token |
Whether to pool ss in accumulated summary between all terms fitted in a linear model (yes , no ); default no |
DENOMINATOR = string token |
Whether to base ratios in accumulated summary on rms from model with smallest residual ss or smallest residual ms (ss , ms ); default ss |
NOMESSAGE = string tokens |
Which warning messages to suppress (dispersion , leverage , residual , aliasing , marginality , vertical , df , inflation ); default * |
FPROBABILITY = string token |
Printing of probabilities for variance and deviance ratios (yes , no ); default no |
TPROBABILITY = string token |
Printing of probabilities for t-statistics (yes , no ); default no |
SELECTION = string tokens |
Statistics to be displayed in the summary of analysis produced by PRINT=summary , seobservations is relevant only for a Normally distributed response, and %cv only for a gamma-distributed response (%variance , %ss , adjustedr2 , r2 , seobservations , dispersion , %cv , %meandeviance , %deviance , aic , bic , sic ); default %var , seob if DIST=normal , %cv if DIST=gamma , and disp for other distributions |
SELINEAR = string token |
Whether to calculate s.e.s for linear parameters when nonlinear parameters are also estimated (yes , no ); default no |
WEIGHTS = variate |
Prior weights for the units |
CMETHOD = string token |
Estimation method (maximumlikelihood , reml ); default maxi |
CPARAMETER = scalars |
Correlation parameter |
CPOSITIONS = variate |
Correlation positions |
CGROUPS = factor |
Groupings of correlation positions |
MAXCYCLE = scalars |
Maximum number of iterations; default 100 |
TOLERANCE = scalars |
Convergence criterion; default 10-5 |
Parameter
TERMS = formula |
Terms to be fitted |
---|
Description
RAR1
allows you to fit regression and nonlinear models to data, such as repeated measurements, where the residuals may follow an AR1 or a power-distance correlation model. The CPOSITIONS
option specifies the coordinates of the observations in the direction (e.g. time) along which the correlation model operates. You can also use the CGROUPS
option to specify a factor to define groups of observations for the model – the correlation model is then defined only over the observations that belong to the same groups. The parameter phi of the AR1 or power-distance model is estimated within RAR1
, and is assumed to be the same for every group. (Note that the model will be AR1 if the observations are each one unit apart within each group – the power-distance model is the natural extension of the AR1 model to unequally-spaced data; see Method.) You can save the estimated value of phi, in a scalar, using the CPARAMETER
option.
Otherwise, RAR1
is used much like FIT
. It must be preceded by a MODEL
statement. You can also give an RCYCLE
statement first if you want to estimate nonlinear parameters. The MODEL
statement must have the WEIGHT
option set to a symmetrix matrix, which need not have any values defined. RAR1
will set the values according to the distances (CPOSITIONS
), groups (CGROUPS
) and estimated parameter phi. These values remain set after RAR1
. So you can display or save further output using RCHECK
, RDISPLAY
, RGRAPH
or RKEEP
, in the usual way. You could also, for example, use RAR1
to fit a full set of regression terms, and then use DROP
to investigate smaller models while still using the phi estimate from the full model. RAR1
has a TERMS
parameter to specify the terms to be fitted, like the parameter of FIT
. It also has options CALCULATION
, CONSTANT
, FACTORIAL
, POOL
, DENOMINATOR
, NOMESSAGE
, FPROBABILITY
, TPROBABILITY
, SELECTION
and SELINEAR
which operate like those of FIT
.
The PRINT
option is also similar, except that it has three additional settings:
cparameter |
prints the estimated value of the correlation phi, together with a test for phi=0, |
---|---|
cmonitoring |
provides monitoring information for the estimation of phi, |
cplot |
plots the likelihood (or REML likelihood) for phi. |
Note, the likelihood values omit some constant terms that depend only on the regression terms. The default is PRINT=model,summary,estimates,cparameter
.
The other options control the estimation. The CMETHOD
option controls whether phi is estimated for regression models by REML or by maximum likelihood (default maxi
); with nonlinear models only maximum likelihood is available. The MAXCYCLE
option defines the maximum number of iterations (default 100) used to estimate phi, and the TOLERANCE
option specifies the convergence criterion i.e. the accurary to which phi is to be estimated (default 10-5).
Options: PRINT
, CALCULATION
, CONSTANT
, FACTORIAL
, POOL
, DENOMINATOR
, NOMESSAGE
, FPROBABILITY
, TPROBABILITY
, SELECTION
, SELINEAR
, WEIGHTS
, CMETHOD
, CPARAMETER
, CPOSITIONS
, CGROUPS
, MAXCYCLE
, TOLERANCE
.
Parameter: TERMS
.
Method
To estimate phi RAR1
uses procedure MIN1DIMENSION
, which calls a procedure _MIN1DFUNCTION
, which is loaded automatically with RAR1
. _MIN1DFUNCTION
uses the FIT
directive to fit the regression model for a particular value of phi, and then evaluates the likelihood or REML likelihood (according to the setting of the CMETHOD
option).
Action with RESTRICT
Restrictions are not allowed.
See also
Directive: VSTRUCTURE
.
Procedure: NLAR1
.
Commands for: Repeated measurements, Regression analysis.
Example
CAPTION 'RAR1 example',!t('Regress daily gas demand on coldness,',\ 'using an AR(1) model for errors, with phi estimated by REML;',\ 'see Guide to Genstat, Part 2, Example 7.4a'); STYLE=meta,plain READ [SETNVALUES=yes] Demand 324.04 333.30 345.96 403.74 391.84 361.36 358.26 356.44 360.60 326.56 341.74 349.14 363.76 352.46 368.34 382.50 381.26 351.14 348.04 359.46 364.76 338.44 339.20 342.06 396.84 418.24 457.46 463.36 440.34 443.80 419.06 390.34 383.14 415.26 449.86 471.84 458.70 408.46 345.34 309.04 283.56 287.36 314.44 303.40 286.16 298.54 308.44 309.16 336.86 337.64 334.10 302.66 303.84 289.94 251.86 239.26 288.84 319.40 311.46 308.74 361.74 390.16 367.76 365.14 364.40 367.56 363.84 340.34 319.76 319.06 322.24 281.10 312.96 295.64 273.74 321.16 313.16 286.64 348.60 359.46 338.94 322.44 338.96 359.26 357.24 404.00 386.56 391.14 411.14 405.46 377.86 371.74 333.20 354.06 319.64 310.04 336.86 301.36 295.24 264.90 312.46 363.34 362.04 340.26 : READ [SETNVALUES=yes] Coldness -33.5 -21.8 -13.8 -12.4 -0.9 -38.7 -32.7 -49.0 -34.2 -59.2 -40.9 -34.8 -29.8 -34.9 -10.8 -26.2 1.6 -50.3 -53.0 -40.5 -32.2 -60.2 -50.5 -47.5 9.1 32.9 42.6 29.2 16.8 6.5 -0.8 -14.6 -14.2 -9.1 8.9 13.8 11.3 -34.1 -67.9 -93.3 -100.9 -91.7 -69.3 -82.8 -79.6 -79.6 -57.4 -74.8 -58.8 -53.0 -63.8 -68.1 -91.1 -76.0 -115.9 -114.2 -93.5 -68.3 -74.9 -78.4 -21.4 -27.1 -38.7 -55.8 -64.1 -46.2 -59.0 -49.7 -59.8 -87.9 -51.5 -90.9 -85.5 -87.5 -94.1 -55.8 -75.7 -104.1 -60.9 -48.9 -59.1 -56.8 -50.3 -59.1 -56.0 -38.7 -13.7 -47.0 -24.1 -31.8 -44.8 -65.4 -84.2 -47.9 -70.2 -98.4 -76.1 -104.2 -97.0 -117.3 -62.0 -44.8 -47.3 -64.3 : CALCULATE nunits = NVALUES(Demand) VARIATE [VALUES=1...nunits] Time SYMMETRIC [ROWS=nunits] wmat MODEL [WEIGHTS=wmat] Demand RAR1 [CMETHOD=reml; CPOSITIONS=Time] Coldness " compare with REML " GROUP Time; Timefactor VCOMPONENTS [FIXED=Coldness; CADJUST=none] Timefactor VSTRUCTURE [TERM=Timefactor] AR; ORDER=1 REML [PRINT=effects,components,deviance] Demand