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CONFID

The CONFID command can be used to compute confidence intervals and a confidence ellipse for two coefficients after model estimation. A confidence interval (CI) can be thought of as a particular kind of interval estimate of a population parameter. It is used to indicate the reliability of an estimate. It is an observed interval (i.e. it is calculated from the observations), in principle different from sample to sample, that frequently includes the parameter of interest if the experiment is repeated. How frequently the observed interval contains the parameter is determined by the confidence level or confidence.

In general, the format is:

Estimation Command e.g. OLS

CONFID vars / options

Following a STAT command, CONFID computes interval estimates for the population mean. Following a regression estimation, CONFID computes interval estimates for coefficients of the variables. The name $SIG2 can be specified to get a confidence interval for the error variance.

The available options are:

OPTION DESCRIPTION
df= Specifies the degrees of freedom to use for obtaining 5% and 10% critical values from the t-distribution. This is typically (N-K). With 2 coefficients this will be the denominator degrees of freedom for obtaining a 5% critical value from the F-distribution.
normal Specifies that the normal distribution rather than the t distribution should be used in computing confidence regions. Often, we only know that the coefficients are asymptotically normally distributed and the use of the t or F distribution would be inappropriate.
tcrit= Specifies the t-distribution critical value for calculating confidence intervals. This value can be obtained from tables of the t-distribution or from output associated with use of the DISTRIB command. If this option is not specified then SHAZAM computes the critical values for 90% and 95% confidence intervals.

When only 2 coefficients are listed, a plot of the confidence ellipse is computed. The available plot options are HOLD, NOBLANK, SYMBOL, WIDE/NOWIDE, XMAX=, XMIN=, YMAX=, and YMIN=. The GRAPH option can be used for a GNUPLOT plot.

Other available options are:

OPTION DESCRIPTION
append Specifies that the gnuplot command file is to be appended to gnuplot command files created with previous commands in the SHAZAM program.
axis By default, an x-axis and y-axis is drawn at x=0 and y=0. Use NOAXIS to omit the axes.
commfile= Gives the filename for the gnuplot command file (8 characters maximum).
device= Specifies the type of device for gnuplot output. The default is the terminal screen. The option DEVICE=POSTSCRIPT sends output to a PostScript file. The gnuplot command set term gives the complete list of valid options.
df= Specifies the degrees of freedom to use for obtaining 5% and 10% critical values from the t-distribution. This is typically (N-K). With 2 coefficients this will be the denominator degrees of freedom for obtaining a 5% critical value from the F-distribution.
fcrit= Specifies the critical value from an F-distribution to be used for the joint confidence region plot. This option is similar to the TCRIT= option and is usually used to complement it. If the FCRIT= option is not specified a 5% critical value will be used.
graph Prepares a gnuplot plot of the joint confidence region when 2 coefficients are specified. For more information on this option see the chapter PLOTS AND GRAPHS. With the GRAPH option the APPEND, AXIS, NOAXIS, COMMFILE=, DEVICE=, OUTPUT= and PORT= options are also available as described for the GRAPH command.
noaxis By default, an x-axis and y-axis is drawn at x=0 and y=0. Use NOAXIS to omit the axes.
nofplot Omits the joint confidence region plot when two coefficients are specified. This option would be used if you only wanted the individual confidence intervals for the coefficients.
nomid Omits the display of a symbol at the center of the confidence ellipse.
notplot Omits the computation of the confidence intervals for individual coefficients. This might be used if only two coefficients were specified and you only want the joint confidence region plot (FPLOT). Normally, the individual confidence intervals are shown on the joint plot with a plus symbol (+) to show the outline of the confidence rectangle. The NOTPLOT option will suppress the drawing of the (+) symbol.
output= Gives the filename for the gnuplot output file (8 characters maximum) when the DEVICE= option is used. When DEVICE=POSTSCRIPT is used the default output filename is GNU.ps.
points= SHAZAM usually constructs the confidence ellipse by evaluating the ellipse at approximately 200-205 points. The number used can be changed with this option if more or fewer points are desired to obtain a better looking plot.
port= Use PORT=NONE to obtain gnuplot command and data files but no gnuplot output.
xmax= Specifies the desired maximum for the X axis. The NOPRETTY option must be used with these options otherwise SHAZAM attempts to make pretty intervals on the axis by checking the range of the data. If this is not specified the computed MAXimum for the variables will be used.
xmin= Specifies the desired minimum for the X axis. The NOPRETTY option must be used with these options otherwise SHAZAM attempts to make pretty intervals on the axis by checking the range of the data. If this is not specified the computed MAXimum for the variables will be used.
ymax= Specifies the desired maximum for the Y axis. The NOPRETTY option must be used with these options otherwise SHAZAM attempts to make pretty intervals on the axis by checking the range of the data. If this is not specified the computed MAXimum for the variables will be used.
ymin= Specifies the desired minimum for the Y axis. The NOPRETTY option must be used with these options otherwise SHAZAM attempts to make pretty intervals on the axis by checking the range of the data. If this is not specified the computed MAXimum for the variables will be used.

In some cases, users would like to compute the confidence region for coefficients that have been estimated in an earlier run and do not wish to re-estimate a model. This is possible for any set of two coefficients where you tell SHAZAM the estimated values of the coefficients, their estimated variances, and the covariance between the coefficients. In this case, the CONFID command does not need to follow an estimation command, but the following options must be included:

OPTION DESCRIPTION
coef1= Specifies the coefficient estimate for the first coefficient you wish to plot. This coefficient will appear on the Y-axis of the plot.
coef2= Specifies the coefficient estimate for the second coefficient you wish to plot. This coefficient will appear on the X-axis of the plot.
covar12= Specifies the estimated covariance between the two coefficients.
df= Specifies the degrees of freedom to use for obtaining 5% and 10% critical values from the t-distribution. This is typically (N-K). With 2 coefficients this will be the denominator degrees of freedom for obtaining a 5% critical value from the F-distribution.
var1= Specifies the estimated variance of the first coefficient.
var2= Specifies the estimated variance of the second coefficient.