Chilimit

Purpose

Chi-squared confidence limits from sum-of-squares residuals.

Synopsis

[lim,scl,dof] = chilimit(ssqr,cl)

lim = chilimit(scl,dof,cl)

cl = chilimit(scl,dof,ssqr,2) %calculate conf. level for ssqr

cl = chilimit(ssqr,new_ssqr,[],2) %calculate conf. level for new_ssqr

Description

CHILIMIT determines a confidence limit for sum-of-squares residuals by fitting the residuals to the g Chi-squared h distribution. If the sum-squared residuals are reasonably approximated by a Chi-squared distribution this gives a very good estimate of the confidence level. However, it has been observed that outliers can significantly bias the estimate.

CHILIMIT can also calculate the confidence level corresponding to a given sum squared residual value (see flag and Calculating Confidence Level below)

Inputs

• ssqr = sum-of-squares residuals (a.k.a. Q)

Optional Inputs

• cl = confidence level (0<cl<1) {default = 0.95}
• flag = indicates if the inverse calculation should be done (=2) or the standard calculation should be done (=1) {default = 1}

Outputs

• lim = calculated limit.
• scl = scaling determined from the residuals.
• dof = degrees of freedom determined from the residuals.

The scaling, (scl), and number of degrees of freedom, (dof), returned from a previous call to CHILIMIT can be used in subsequent calls to CHILIMIT to obtain new limits without the original residuals.

Calculating Confidence Level

The inverse of chilimit must be called with four inputs using the scaling, degrees of freedom, ssqr, and the flag indicating that the inverse calculation should be done.

cl = chilimit(scl,dof,ssqr,2);

where the inputs (scl) and (dof) are outputs described above. The input (ssqr) corresponds to a sum-of-squared residual and the input 2 is a flag that tells the algorithm to calculate the inverse.

See Also

chitest, distfit, jmlimit, pca, pcr, plotqq, pls, residuallimit