Adds extra terms to a linear, generalized linear, generalized additive or nonlinear model.

### Options

`PRINT` = string tokens |
What to print (`model` , `deviance` , `summary` , `estimates` , `correlations` , `fittedvalues` , `accumulated` , `monitoring` , `confidence` ); default `mode, summ, esti` |
---|---|

`NONLINEAR` = string token |
How to treat nonlinear parameters between groups (`common` , `separate` , `unchanged` ); default `unch` |

`CONSTANT` = string token |
How to treat the constant (`estimate` , `omit` , `unchanged` , `ignore` ); default `unch` |

`FACTORIAL` = scalar |
Limit for expansion of model terms; default `*` i.e. that in previous `TERMS` statement |

`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` , `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 |

`PROBABILITY` = scalar |
Probability level for confidence intervals for parameter estimates; default 0.95 |

`AOVDESCRIPTION` = text |
Description for line in accumulated analysis of variance (or deviance) table when `POOL=yes` |

### Parameter

formula |
List of explanatory variates and factors, or model formula |
---|

### Description

`ADD`

adds terms to the current regression model, which may be linear, generalized linear, generalized additive, standard curve or nonlinear. It is best to give a `TERMS`

statement before investigating sequences of models using `ADD`

, in order to define a common set of units for the models that are to be explored. If no model has been fitted since the `TERMS`

statement, the current model is taken to be the null model.

The model fitted by `ADD`

will include a constant term if the previous model included one, and will not include one if the previous model did not. You can, however, change this using the `CONSTANT`

option.

The options of `ADD`

are almost all the same as those of the `FIT`

directive, and are described there. There is also an extra option `NONLINEAR`

. This is relevant when fitting curves. For example, if we have a variate `Dilution`

and a factor `Solution`

, the program below will fit parallel curves for the different solutions.

`MODEL Density`

`TERMS Dilution * Solution`

`FITCURVE [PRINT=model,estimates; CURVE=logistic]\`

` Dilution + Solution`

If we then put

`ADD Dilution.Solution`

the curves are still constrained to have common nonlinear parameters, but all linear parameters are estimated separately for each group. Alternatively, if we put

`ADD [NONLINEAR=separate] Dilution.Solution`

different nonlinear parameters will be estimated for each solution too; so only the information about variability is pooled.

Options: `PRINT`

, `NONLINEAR`

, `CONSTANT`

, `FACTORIAL`

, `POOL`

, `DENOMINATOR`

, `NOMESSAGE`

, `FPROBABILITY`

, `TPROBABILITY`

, `SELECTION`

, `PROBABILITY`

, `AOVDESCRIPTION`

.

Parameter: unnamed.

### Action with `RESTRICT`

If a `TERMS`

statement was given before fitting the model, any restrictions on the variates or factors in the model will have been implemented then. So any restrictions on vectors involved in the model specified by `ADD`

will be ignored. If no `TERMS`

statement has been given and `ADD`

introduces new terms into the model, restrictions on the variates or factors in these terms will be taken into account and may cause the units involved in the regression to be redefined.

### See also

Directives: `MODEL`

, `TERMS`

, `FIT`

, `FITCURVE`

, `DROP`

, `SWITCH`

, `TRY`

.

Functions: `COMPARISON`

, `POL`

, `REG`

, `LOESS`

, `SSPLINE`

.

Commands for: Regression analysis.

### Example

" Example FIT-2: Multiple linear regression Relate the monthly water usage (thousand gallons) of a production plant to four variables: 1. Average monthly temperature (degrees F) 2. Amount of production (billion pounds) 3. Number of plant operating days in the month 4. Number of people employed (Data from Draper and Smith, Regression Analysis (1981) p353.)" " The data from 17 months are in a file called 'FIT-2.DAT' and names for the data columns are on the first line" FILEREAD [NAME='%gendir%/examples/FIT-2.DAT'; IMETHOD=read] FGROUP=no " Specify that the amount of water used is to be the response variable, and print the correlation matrix of all the variables. The TERMS directive also allows use of the directives ADD, DROP and so on, to compare alternative sets of explanatory variables." MODEL Water TERMS [PRINT=correlations] Temp,Product,Opdays,Employ " Fit a linear regression of water usage on amount of production, since this variable is most highly correlated with water usage (0.631)." FIT Product " Water use increases by 80 gallons (s.e. 25) for each extra billion pounds of production - ignoring the effect of other variables." " Regress water usage on all the explanatory variables, to take account of the smaller effects." ADD Temp,Opdays,Employ " All the variables have a significant effect on water usage (all the t statistics are large). The effect of increasing production by a billion pounds while keeping the other variables constant is to increase water usage by 212 gallons (s.e. 46)." " The first month is particularly influential. Display all the fitted values, residuals and leverages (influence). " RDISPLAY [PRINT=fitted] " Display the relationship between water usage and production, adjusting for the other effects" RGRAPH [GRAPHICS=high] Product " Plot the residuals against the fitted values to see if there is any indication of non-constant variance" RCHECK [GRAPHICS=high] residual; fitted