Fits regression models to validate predictions, for example from a deterministic model, against observed data (R.W. Payne).
|What to print (
||What to print from the regressions (
||Whether to base ratios in accumulated summary on rms from model with smallest residual ss or smallest residual ms (
||Which warning messages to suppress (
||Printing of probabilities for variance and deviance ratios (
||Printing of probabilities for t-statistics (
||Statistics to be displayed in the summary of analysis produced by
||Probability level for confidence intervals for parameter estimates; default 0.95|
||Predictions from the model|
||Saves information from the analysis|
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.
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.
RPRINT option controls the output from the regression analyses requested by 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
PROBABILITY options operate like those of
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
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.
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
PREDICTIONS can be restricted to analyse a subset of the data.
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