Fits locally weighted regression models (loess) to data with groups (D.B. Baird).
Options
PRINT = string tokens |
What to print (model , deviance , summary , estimates , correlations , fittedvalues , accumulated , monitoring , confidence , groups , submodels ); default mode , summ , esti |
PLOT = string tokens |
What to plot (fittedvalues , residuals ); default * – no plots |
FINALMODEL = string token |
What to model to fit as the final model (common , parallel , separateslopes , full ); default full |
CONSTANT = string token |
How to treat the constant (estimate , omit ); default esti |
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 |
PROBABILITY = scalar |
Probability level for confidence intervals for parameter estimates; default 0.95 |
MAXCYCLE = scalar |
Maximum number of iterations for the back-fitting algorithm; default 100 |
DEVIANCE = scalar |
Saves the residual deviance |
DF = scalar |
Saves the residual d.f. |
Parameters
X = variate |
Explanatory x-variate to be fitted |
GROUPS = factor |
Groups to be fitted |
SMOOTH = scalar |
Smoothing value to be used in the loess term; default 4 |
SMTYPE = string token |
Type of value provided in SMOOTH (df , smoothing ); default df |
ORDER = scalar |
Order of regression used in loess term (1 or 2); default 1 |
RESIDUALS = variates |
Simple residuals from the fitted loess model |
FITTEDVALUES = variates |
Fitted values from the fitted loess model |
ACCUMULATED = pointer |
Saves the accumulated analysis-of-variance (or deviance) table as a pointer with a variate or text for each column (source, d.f. etc.) |
SAVE = pointer |
Save structure for the fitted model |
Description
RLOESSGROUPS
is provided to allow the full interaction between a loess smooth on an explanatory variate X
and a factor GROUPS
to be fitted. It is not possible to include LOESS(X)*GROUPS
in the TERMS
directive, so the procedure loops around the groups to fit individual models for each group, and then combines the results.
The use of RLOESSGROUPS
is similar to FIT
. It must be preceded by a MODEL
statement, and can be followed by RDLOESSGROUPS
and RKLOESSGROUPS
to display and save the results, which operate similarly to RDISPLAY
and RKEEP
respectively. It also has options PRINT
, CONSTANT
, DENOMINATOR
, NOMESSAGE
, FPROBABILITY
, TPROBABILITY
and PROBABILITY
that operate like those of FIT
. However, the PRINT
option has two extra settings: submodel
to print the three submodels (explained below), and groups
to print the individual fits for each group. The output from each submodel or group will use the other settings of PRINT
.
The form of the loess curve can be specified by the SMOOTH
, SMTYPE
and ORDER
parameters which specify the arguments to the LOESS
function. If SMTYPE=df
, SMOOTH
gives the number of degrees of freedom used in the function (which should be 2 or greater), while if SMTYPE=smooth
, SMOOTH
gives the smoothing parameter (which should be between 0 and 1). The ORDER
parameter is 1 for a linear loess model and 2 for a quadratic one.
RLOESSGROUPS
fits a sequence of models, starting with a common line (ignoring the groups). The next, parallel, model fits a common slope and loess curve, but different intercepts for the groups. The third model (separate slopes) has a common loess curve but different slopes and intercepts. Finally, the fourth (full) model has different loess curves, slopes and intercepts. Groups with less than four observations should be restricted out when fitting the full model, as these cannot be fitted by a loess model. To fit the full model, RLOESSGROUPS
uses SUBSET
to break up the data into separate groups. It fits these individually using FIT
, and then combines the results. The results of these individual fits are printed only if the groups
setting is included in the PRINT
option.
The FINALMODEL
option specifies how far to take the sequence of models, with settings common
, parallel
, separateslopes
and the default, full
, corresponding to the models just described. Results from the models earlier than the requested final model are printed only if the submodels
setting is included in the PRINT
option. Further output displayed by RDLOESSGROUPS
and information saved by RKLOESSGROUPS
will only be from the final model.
The DEVIANCE
option saves the residual deviance, and the DF
option saves the residual number of degrees of freedom. The RESIDUALS
and FITTEDVALUES
parameters save the residuals and fitted values, respectively. The ACCUMULATED
parameter saves the accumulated analysis-of-variance (or deviance) table as a pointer. The suffixes of ACCUMULATED
for the last 4 columns in the pointer depend on whether it is an analysis of variance ('s.s.'
, 'm.s.'
, 'v.r.'
, 'F pr.'
) or an analysis of deviance table ('deviance'
, 'mean dev.'
, 'dev. r.'
, 'approx F pr.'
).
The SAVE
parameter can save a pointer, with information about the analysis, for use by the procedures RDLOESSGROUPS
and RKLOESSGROUPS
.
Options: PRINT
, PLOT
, FINALMODEL
, CONSTANT
, DENOMINATOR
, NOMESSAGE
, FPROBABILITY
, TPROBABILITY
, PROBABILITY
, MAXCYCLE
, DEVIANCE
, DF
.
Parameter: X
, GROUPS
, SMOOTH
, SMTYPE
, ORDER
, RESIDUALS
, FITTEDVALUES
, ACCUMULATED
, SAVE
.
Method
RLOESSGROUPS
uses SUBSET
to break the data into separate groups and fits these individually using FIT
, and then combines the results. The 3 sub-models are fitted first using the usual TERMS
and FIT
directives so obtain the accumulated analysis-of-variance (or deviance) table. The model with separate slopes may be dropped if this has negative sums of squares.
Action with RESTRICT
As in FIT
, the y-variate (specified in an earlier MODEL
directive) can be restricted to analyse a subset of the data.
See also
Directives: FIT
, MODEL
, TERMS
.
Procedures: RDLOESSGROUPS
, RKLOESSGROUPS
.
Commands for: Regression analysis.
Example
CAPTION 'RLOESSGROUPS example',\ 'Yield of sugar beet vs soil phosphate in 4 years'; STYLE=major,plain FACTOR [LEVELS=4; VALUES=16(1...4)] Year OPEN '%EXAMPLES%/GuidePart2/beet.dat'; CHANNEL=2 READ [PRINT=*; CHANNEL=2] Beetwt,%sugar,SoilP CLOSE 2 CALCULATE Sugar = Beetwt * %sugar / 100 MODEL Sugar RLOESSGROUPS [PRINT=model,summary,estimates,accumulated; \ PLOT=residuals,fitted; FPROB=yes; TPROB=yes] \ SoilP; GROUP=Year; SMOOTH=2