Fits regression models to validate predictions, for example from a deterministic model, against observed data (R.W. Payne).

### Options

`PRINT` = string tokens |
What to print (`summary` , `tests` , `nullmodel` , `slopeone` , `constantzero` , `fullmodel` ); default `summ` , `test` |

`RPRINT` = string tokens |
What to print from the regressions (`model` , `deviance` , `summary` , `estimates` , `correlations` , `fittedvalues` , `accumulated` , `monitoring` , `confidence` , `graph` , `checks` ); default `mode` , `summ` , `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` |

`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 |

### Parameters

`OBSERVATIONS` = variates |
Observed data |

`PREDICTIONS` = variates |
Predictions from the model |

`SAVE` = pointers |
Saves information from the analysis |

### Description

`RVALIDATE`

fits several regression models to help assess the validity of a deterministic model. The `OBSERVATIONS`

parameter supplies a variate of observed data, and the `PREDICTIONS`

parameter supplies a variate with corresponding predictions from the model. If the model is in correct agreement with real life, the relationship between these variates should be explained by the null model consisting of a line with slope one through the origin. Alternatively, if the model shows a consistent bias, the relationship could be explained by a line with slope one, and with a non zero intercept (or constant). The third possibility, which might arise from an incorrect calibration, would be to have a zero constant with the slope no longer equal to one. The final possibility, indicating discrepancies in both constant and slope, would be an ordinary repression line (i.e. the full model). `RVALIDATE`

fits these models in turn, and calculates tests to assess whether the constant differs from zero, and the slope differs from one.

The `PRINT`

option specifies what output is required, with settings:

`summary`

gives a summary of the analyses, showing the parameter estimates and their standard errors, together with the residual sum of squares, degrees of freedom and mean squares from each model;

`tests`

tests to assess whether the constant differs from zero, and the slope differs from one;

`nullmodel`

output from the model with constant zero and slope one;

`slopeone`

output from the model with slope one and a non-zero constant;

`constantzero`

output from the model with constant zero and slope not equal to one;

`fullmodel`

output from the model with a non-zero constant and a slope not equal to one.

The `RPRINT`

option controls the output from the regression analyses requested by the `PRINT`

option. It has the same settings as the `PRINT`

option of the `FIT`

directive, and two additional settings: `graph`

plots the line and the data, and `checks`

provides the standard plots of the residuals (using the `RCHECK`

procedure). The `DENOMINATOR`

, `NOMESSAGE`

, `FPROBABILITY`

, `TPROBABILITY`

, `SELECTION`

and `PROBABILITY`

options operate like those of `FIT`

.

The `SAVE`

parameter can save a pointer containing elements with the following labels:

`Summary`

pointer saving the summary of the analyses, containing a text with the names of the models, and then variates for the parameter estimates, their standard errors, the residual sum of squares, degrees of freedom and mean squares from each model;

`Tests`

pointer saving the tests, containing a text to describe the test, and them variates with sums of squares, degrees of freedom, mean squares, variance ratios and F probabilities;

`Null model`

regression save structure from the model with constant zero and slope one;

`Slope one`

regression save structure from the model with slope one and a non-zero constant;

`Constant zero`

regression save structure from the model with constant zero and slope not equal to one;

`Full model`

regression save structure from the model with a non-zero constant and a slope not equal to one. When `RVALIDATE`

defines the pointer, the `CASE`

and `ABBREVIATE`

options of the `POINTER`

directive are set to enable the labels to be abbreviated and specified in either lower case, or upper case, or any mixture.

Options: `PRINT`

, `RPRINT`

, `DENOMINATOR`

, `NOMESSAGE`

, `FPROBABILITY`

, `TPROBABILITY`

,

`SELECTION`

, `PROBABILITY`

. Parameters: `OBSERVATIONS`

, `PREDICTIONS`

, `SAVE`

.

### Method

Ignoring the options, the models are fitted by the following commands.

" null model: slope one, constant zero " MODEL [OFFSET=PREDICTIONS] OBSERVATIONS FIT [CONSTANT=omit] " slope one, constant estimated " MODEL [OFFSET=PREDICTIONS] OBSERVATIONS FIT " constant zero, slope estimated " MODEL OBSERVATIONS FIT [CONSTANT=omit] PREDICTIONS " full model: slope & constant estimated " MODEL OBSERVATIONS FIT PREDICTIONS

### Action with `RESTRICT`

`OBSERVATIONS`

and `PREDICTIONS`

can be restricted to analyse a subset of the data.

### See also

Directive: `FIT`

.

Procedure: `BLANDALTMAN`

.

Commands for: Regression analysis.

### Example

CAPTION 'RVALIDATE example'; STYLE=meta READ Observed,Predicted 16.15 16.32 15.04 16.15 12.66 14.96 18.93 18.45 18.36 19.72 17.17 16.83 18.53 19.72 17.43 18.19 16.23 18.11 18.61 20.06 18.92 18.19 11.90 12.24 17.09 17.85 18.70 12.75 16.41 16.66 18.98 18.02 18.79 17.00 10.71 12.58 17.94 17.34 14.54 15.89 18.61 11.90 12.49 14.79 19.46 19.97 18.27 17.51 17.68 19.80 16.49 16.15 16.15 16.91 15.98 16.91 16.06 17.00 15.55 16.74 18.61 16.83 16.91 17.00 12.32 14.79 17.68 19.80 16.06 16.83 18.49 19.29 19.97 19.29 15.54 16.66 22.04 19.38 15.21 16.23 16.32 15.89 18.61 16.74 22.86 19.89 7.68 9.27 : RVALIDATE [PRINT=summary,tests,nullmodel,slopeone,constantzero,fullmodel;\ RPRINT=model,summary,estimates,confidence,graph]\ Observed; PREDICTIONS=Predicted