Tsqlim

Purpose

Calculates PCA confidence limits for Hotelling's T², or calculates the confidence level corresponding to given a Hotelling's T² value and the corresponding model information.

Synopsis

tsqcl = tsqlim(m,pc,cl)

tsqcl = tsqlim(model,cl)

cl = tsqlim(m,pc,tsq,2);

cl = tsqlim(model,tsq,2);

Description

Inputs can be in one of two forms:

(a) the number of samples m, the number of principal components used pc, and the fractional confidence limit, cl (0 < cl < 1) which can be a scalar or a vector (to calculate multiple confidence limits simultaneously).

or (b) a standard model structure, model, and the fractional confidence limit, cl (0 < cl < 1).

The output tsqcl is the confidence limit based on an F distribution as shown below. See Jackson (1991).

    $T_{K,M,\alpha }^{2}={\frac {K\left(M-1\right)}{M-K}}{{F}_{K,M-K,\alpha }}$

where $K$ is the number of PCs, $M$ is the number of samples and ${{F}_{K,M-K,\alpha }}$ is the F distribution with $K$ degrees of freedom in the numberator and $M-K$ degrees of freedom in the denominator, and probability point $\alpha$.

Inputs

• m = the number of samples.
• pc = the number of PCs.
• cl = the confidence limit (cl) where 0 < cl < 1.

Optionally, (m) and (pc) can be omitted and a standard model structure (model) can be passed along with the confidence limit (cl).

Optional Inputs

• flag = [ {1} | 2 ] governs how the function is called. 1 = calculates the T^2 at the CL (default), 2 = calculates the CL from an input T^2 (tsq) (This is similar to how FTEST is used) When flag=2,

Outputs

• tsqcl = the confidence limit. (See optional input flag for the inverse calculation.)

Examples

tsqcl = tsqlim(15,2,0.95)

model = pca(data,pc); tsqcl = tsqlim(model,0.95)

See Also

analysis, chilimit, pca, pcr, pls, subgroupcl