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### Special rules for the value of attributes concerning parallel derivation of production functions – or staircase function with partial correlation instead of regression

Leading article: 2021. June (MIAU No. 274.)
(Previous article: MIAU No. 273.)

Keywords: regression, additivity, multiplicativity, impact, similarity analysis, partial correlation

Abstract: The naïve modelling experts think, models will become better if more attributes (Xi) with (as far as possible higher) positive correlation values (compared to Y) can be involved into a model. Therefore, it seems to be that the attributes (Xi) with the most negative correlations are the less useful attributes to derive a production function for a Y-attribute. It is the same effect as in case of ships, which could only be used for centuries if the wind comes from behind – and suddenly the appropriate technique as such got identified. Unfortunately, the regression models (being since ever the fundamental solution in modelling challenges) can really intagrate attributes (Xi) with a higher probability when the correlation values (compared to Y) are positive and as higher as possible. All this is but not valid for the similarity analyses (for the staircase functions). The models with double attribute-sets are even capable of domesticating useless polynomial effects. In case of staircase functions, it is to derive, that the primary correlation value of a production function between the facts and estimations can be increased if (in case of a lot of Xi) the attributes of the first selection are hidden and based on this step-by-step logic more parallel production functions can be built – while each single attribute belongs to a production function AND a new production function will be created based on the estimations (Xi) of the parallel models. Even, the primary layer (estimation) and therefore each of its attributes can be excluded from the modelling process and the correlation value is still higher than in case of the primary model with the first selection of (“full-blood”-) attributes. The number of the full-blood-attributes can also be higher than the number of such (half-blood) attributes which are used for the less robust production functions in a direct way – and these quasi useless attributes lead to the quasi same high correlation values as the full-blood-attributes after the first selection phase – in form of more alternative solutions. Therefore, the value of an attribute depends on the involved modelling methods/techniques and not directly from the correlation between Xi and Y (c.f. from coal powder can diamond be pressed). All these are valid for additive models. The alternatives, the multiplicative models can not exclude attributes in a way where the parameters will be set to zero because one single multiplication with null leads to null independent from each further attribute. So, the multiplicative models always reflect the basic rule: each attribute should always have a connection to each other attribute. The invalidity of the naïve rule about correlation and usefulness can be proven based on one single case study where a random-like input OAM can demonstrate the above-mentioned results. The paper presents this successful case study – where the first analysis led to the needed evidence at once. Based on this evidence, the attributes may not be interpreted from now on as before. If the new higher correlation level is arbitrary near to 1.000, then a new aspect of the modelling should be focused (c.f. STEP-IX-logic as an alternative approximation of the fuzzy-logic) – in order to be capable of talking about robustness of the modelling. Finally, the bridge between the naïve logic and the explored evidence is the term of the partial correlation. This is only valid in case of staircase functions and not in case of regression models. The partial correlation makes possible that an attribute with highly negative (full) correlation value may deliver a highly positive (partial) correlation value if only parts of the known values will be interpreted. More (DOC) *** More (PDF)