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# RLOESSGROUPS procedure

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.

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