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# FITINDIVIDUALLY procedure

Fits regression models one term at a time (R.W. Payne).

### Options

`PRINT` = string tokens What to print (`model`, `deviance`, `summary`, `estimates`, `correlations`, `fittedvalues`, `accumulated`, `monitoring`, `confidence`); default `mode`, `summ`, `esti` How to treat the constant (`estimate`, `omit`); default `esti` Limit for expansion of model terms; default 3 Whether to pool ss in accumulated summary between all terms fitted in a linear model (`yes`, `no`); default `no` Whether to base ratios in accumulated summary on rms from model with smallest residual ss or smallest residual ms (`ss`, `ms`); default `ss` Which warning messages to suppress (`dispersion`, `leverage`, `residual`, `aliasing`, `marginality`, `vertical`, `df`, `inflation`); default `*` Printing of probabilities for variance and deviance ratios (`yes`, `no`); default `no` Printing of probabilities for t-statistics (`yes`, `no`); default `no` 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 level for confidence intervals for parameter estimates; default 0.95 Saves the residual deviance Saves the residual d.f. Whether to use observations with replicated values of the explanatory variables to split the final residual term into a ‘true’ residual and lack of fit (`estimate`, `omit`); default `omit`

### Parameter

`TERMS` = formula Terms to be fitted

### Description

`FITINDIVIDUALLY` is provided as an alternative to the `FIT` directive for use, in particular, with generalized linear models. With these models, for efficiency, the entire model is fitted at once rather than one term at a time as in ordinary regression models. As a result the terms of the generalized linear model are pooled into a single line in the analysis of deviance table. However, if you want to see the contributions of the individual terms in the analysis of deviance table, you can use `FITINDIVIDUALLY` instead of `FIT`.

`FITINDIVIDUALLY` is used exactly like `FIT`. It must be preceded by a `MODEL` statement, and can be followed by `RCHECK`, `RDISPLAY`, `RGRAPH`, `RKEEP`, `ADD`, `DROP`, `SWITCH` and so on. It has a `TERMS` parameter to specify the terms to be fitted, like the parameter of `FIT`. It also has options `PRINT`, `CONSTANT`, `FACTORIAL`, `POOL`, `DENOMINATOR`, `NOMESSAGE`, `FPROBABILITY`, `TPROBABILITY`, `SELECTION` and `PROBABILITY` which operate like those of `FIT`.

If you have observations with replicated values of the explanatory variables, you can set option `LACKOFFIT=estimate` to split the final residual term into a “true” residual (measured by the variation amongst the replicate observations) and lack of fit. `FITINDIVIDUALLY` then sets the dispersion parameter and its number of degrees of freedom in the regression save structure to the “true” residual deviance and its degrees of freedom, so that these will be used for standard errors and probabilities etc. in future output. (These are the aspects that you can set using the `DISPERSION` and `DFDISPERSION` options of `MODEL`.) The `DEVIANCE` option allows you to save the residual deviance, and the `DF` option saves the residual number of degrees of freedom.

Options: `PRINT`, `CONSTANT`, `FACTORIAL`, `POOL`, `DENOMINATOR`, `NOMESSAGE`, `FPROBABILITY`, `TPROBABILITY`, `SELECTION`, `PROBABILITY`, `DEVIANCE`, `DF`, `LACKOFFIT`.

Parameter: `TERMS`.

### Method

`FITINDIVIDUALLY` uses `FCLASSIFICATION` to break the `TERMS` formula up into individual terms. It fits these individually using `ADD`, and then calls `RDISPLAY` to display the output. It uses procedure `FACCOMBINATIONS` to identify the observations with replicated values of the explanatory variables so that it can calculate the lack of fit. It calls an auxiliary procedure `_FITIRSET` for setting the dispersion parameter and its number of degrees of freedom in the regression save structure (this uses inside knowledge of the structure of the structure).

### 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.

Directive: `ADD`, `FIT`.

Commands for: Regression analysis.

### Example

```CAPTION   'FITINDIVIDUALLY example',\
!t('Analysis of the damage caused by waves to forward sections',\
'of cargo-carrying ships (McCullagh & Nelder 1989, page 204).');\
STYLE=meta,plain
FACTOR    [NVALUES=40; LABELS=!T(A,B,C,D,E)] Type
&         [LABELS=!T('1960-64','1965-69','1970-74','1975-79')] Construction
&         [LABELS=!T('1960-74','1975-79')] Operation
GENERATE  Type,Construction,Operation
VARIATE   [NVALUES=40] Service,Damage
127  0     63  0   1095  3   1095  4  1512  6   3353 18  * *  2244 11
44882 39  17176 29  28609 58  20370 53  7064 12  13099 44  * *  7117 18
1179  1    552  1    781  0    676  1   783  6   1948  2  * *   274  1
251  0    105  0    288  0    192  0   349  2   1208 11  * *  2051  4
45  0      0  0    789  7    437  7  1157  5   2161 12  * *   542  1 :
" Use the log of the number of months of service as an offset in the
model; CALCULATE turns zeroes into missing values, which will then
be excluded by TERMS as required for a correct analysis."
CALCULATE Logservice = LOG(Service)