What is an intrinsic value for laypeople

Internet publication for general and integrative psychotherapy
IP-GIPTDAS = 15.12.2000 Internet first edition, last change 13.4.6
Imprint: Graduated psychologists Irmgard Rathsmann-Sponsel and Dr. phil. Rudolf Sponsel
Stubenlohstrasse 20 D-91052 Erlangen * Mail: [email protected]_ Citation & Copyright

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Welcome to the Department of Philosophy of Science, Methodology and Statistical-Mathematical Methods in General and Integrative Psychology, Psychodiagnostics and Psychotherapy here is an overview of:

For non-methodologists and numerical laypeople:
what is important with correlation matrices?
Cross-reference: Main page for those interested in the profession

 
The most important thing in a single sentence: Correlation matrices must not have a large negative Eigenvalue (> = | 0.05 |), otherwise they derail maliciously, contain and produce nonsense.

In a standard matrix analysis, which field provides information about possible negative eigenvalues?:
The summary / Result abstract line allows an immediate orientation at a glance as to how things are going with the numerical stability of a matrix. Here is the most important field NumS. If there are two minus signs and a number, it means that the matrix contains negative eigenvalues ​​- as many as the number indicates - and is to be regarded as derailed (indefinite, "psychotic") and thus produces nonsensical values. Such a matrix is possibly "treatable" if the negative eigenvalues ​​are close to 0 (rule of thumb: <= | 0.02 |).

Notice: Matrices that look like correlation matrices, i.e. are square and symmetrical, have a 1 in the main diagnostic and otherwise for all values ​​<= | 1 | is then no Correlation matrices if they contain only one negative eigenvalue, even if this is only small.

 
Correlation matrices must be formed according to the rules of mathematics (numerical linear algebra), otherwise they can contain a lot of nonsense, although the correlation matrix looks quite normal on the outside and as one is used to: There are the same number of rows and columns (square matrix) and the The upper triangular matrix is ​​mirrored on the main diagonal - from top left to bottom right - which consists of all ones (symmetrical matrix).

Just as very typical and unique genes belong to every human being, so to every correlation matrix there belong very typical and characterizing values, which one can Eigenvalues is called. Every correlation matrix can now be converted into their Eigenvalues disassemble.
It is allowed with "healthy" and "normal" correlation matrices no negative eigenvalues give. A correlation matrix that is negative Eigenvalues contains, can derail maliciously and produce or contain a wide range of mathematical nonsense.
Matrices with negative eigenvalues ​​are called "indefinite" in mathematics. Of these "indefinite" correlation matrices there are now "malignant" ones that can no longer be repaired ("treated") and "benign" ones that have a positive meaning (regularity, functional relationship, linear dependency = collinearity) and that can be repaired "therapy") (such as: Sponsel 1994, Chapter 5).

Benign-indefinite correlation matrices: If the negative eigenvalues ​​are small (approximately | 0.02 |), then they mean that there is a regularity in the correlation matrix and the derailment is likely to be caused by rounding errors and computational inaccuracies in most cases.

Malicious-indefinite correlation matrices: If the negative eigenvalues ​​are large (approximately> | 0.05 |), and the more, the worse, then this means that serious data processing errors have been made (the most common are wrong missing data solutions, impermissible corrections, Mixtures of different samples or different sample sizes in raw data processing; more precise Sponsel 1994, Chapter 3).


Fn_01 Sponsel, Rudolf & Hain, Bernhard (1994). Numerically unstable matrices and collinearity in psychology. Diagnosis, relevance & utility, frequency, etiology, therapy. Erlangen: IEC-Verlag.
Vol. 2: Sponsel, R. (2005). Almost collinearity in correlation matrices with eigenvalue analyzes recognize supplementary volume - volume II
Recognize almost collinearity in correlation matrices with eigenvalue analyzes. Erlangen: IEC-Verlag.



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Cross references
Location: For non-methodologists and numerical laypeople: what is important with correlation matrices?
For those interested in the profession: Abbreviations, definitions, explanations and meanings for standard (correlation) matrix analyzes (SMA).
For non-methodologists and laypeople: what is important with correlation matrices_
Overview and distribution page: Numerically unstable matrices and collinearity in psychology - Ill-Conditioned Matrices and Collinearity in Psychology - Diagnosis, relevance & utility, frequency, etiology, therapy.
Recognize almost collinearity in correlation matrices with eigenvalue analyzes.
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Citation
Sponsel, Rudolf (DAS). For non-methodologists and numerical laypeople: what is important with correlation matrices. Information on general and integrative psychology, psychodiagnostics and psychotherapy. IP-GIPT. Erlangen: https://www.sgipt.org/wisms/nis/nis_laien.htm
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