Hi, Thank you for your help.. (I will try to concretely describe the problem) Yes, those 3 variables are mutually highly correlated (r = 0,70 to max. 0,85), because they describe 3 different colour characteristics (L*, a*, b*) change in dependence of fish fillets salting time (2 hours, 4 and 6 hours).. We know that in system with high salt concentration, muscle tissue will release water, and "absorb" salt, and there is colour changes - those 3 colour variable are also in high correlation with water and salt content in fish muscle during process... (In this content, i will not describe other measured Y variables that are related to study) Changes in water & salt content are most important physicochemical characteristic that allow us to "monitor" microbiological stability of these products, so that will be safe for human consumption.. My goal of stat. analysis is to predict water & salt content from 3 colour variable, or to be more precise, to introduce possibility for industrial usage...I was first tried used a canonical correlation analysis, then PLS and Correlated Component Regression (in XLSTAT) After consulting with XLSTAT staff, they told me: "Unfortunately, the PLSR and CCR are not solutions for residual heteroscedasticity and/or autocorrelation of residuals", which are issues in my reg. models.. After that, i was tried to use discrim. function (from MANOVA) that combine those 3 colour variable, and use this function as predictor...or (don't know) maybe using a neural network model will resolve problem in the best way with max. predicting capability ?? Tnx, Tomislav ... View more

Thank you for your professional assistance, I will certainly do analysis with two randomly disjoint data sets, but there is another " problem " that gives me a bad headache..... When i calculate scores for discrim. functions via MANOVA, i get two stat. signific. function, but 1st (DF) function explain 92% of variance... A priori regression analysis, i was plotted Y-variable against isolated 1st DF, and i get some exponential relationship..i don't know how to set up equation for that relationship (picture 1 in attachment) and how to interpret regress. results On the other hand, i tried to get one component (from 3 original variable) via PCA, and 84 % of variance was extracted from them.. (i don't know whether is this correct way of using PCA in order to isolate only one component) Plotting Y variable against PCA, i get "quadratic" relationship (picure 2)..this is now much easier for me to work with,..... How to do everything stat. correctly, but not to complicate due to theoretical basis of the scientific field and analysis objective? Tnx, Tomislav ... View more

Anyway.. i'm very appreciate for your help Steve..tnx.. Tomislav ... View more

Once again, i need your professional advice.... Does structural equation modelling approach might be a better solution for examination of the relationship between the sets of dependent variables (attached picture in previous post) in 3x2x2 factorial desing, in relation to previous comments about pls regression? Tnx. ... View more

There is something strange to me in this....It seems that she wants to examine (at first) how many FA or PC to retain in model...then, suddenly she said that model with one extracted PC is acceptable..?? ... View more

Use google to find paper "Determining the Number of Factors to Retain in EFA: an easy-to-use computer program for carrying out Parallel Analysis" And, from this web-site you can download SAS macro for parallel analysis....Programs for Number of Components ... View more

I am not a statistician, but according to the literature, I think the best way to determine the number of factors or principal components for analysis is to conduct the parallel analysis.. ... View more

Thank you both for your help and constructive criticism .. Instead MANOVA in first part, I used a three-way ANOVA because small sample size per cell, and the inability to test homogeneity of variance-covariance matrices... (I was thinking before about using factorial MANOVA on principal components, but parallel analysis tells me (for physico-chemical properties) that I can extract only one component ... but when I use the Kaiser-Guttman 'Eigenvalues ​​greater than one" rule, the PCA extracted two components that are with the use of non orthogonal rotation (direct oblim. and  promax) in a very weak correlation required for MANOVA) For examination of the relationship between the sets of dependent variables..I do not know, might not be a bad idea (instead pls) to use a structural equation modelling techniques and mediation model.. ... View more

Thank you Steve for the generous help.. Response surface regression is often used in my area of science, especially in research involving for example the effect of pressure, temperature on certain properties of the substances...in my case, X2 variable is pure categorical (1 = yes, 2 = no), while x1 and x3 are continuous in nature... If I'm not mistaken, I can use this method to predict Y7-Y9 from Y1-Y6 but only through X1 and X3 .... what do you think, whether it would be better to use the PLS regression, but for each level of X1,X2,X3 separately?? Tnx ... View more

upss...p-value of Levene test is higly signif.. ... View more

Once again, thank you Steve your help.... There is one important thing that i forgot to mention in the last query about stat. significant interactions with no theoretical meaning....partial omega square for this effects is relative high (0,4 - 0,6), but p-value of Levene test for this design is highly non-significant    (1E-10)...because this and small sample size, i decide (for ANOVA) to lower my alpha level from 0,05 to 0,01 to compensate for type-1 error... As a result of this, previously signif. interactions is now stat. non-significant....I hope that I have acted in accordance with the rules of statistics Best wishes, Tomislav ... View more

Steve, thank you for your help....but once again I need your professional advice.... In 3-way ANOVA, i have some statistically significant interaction with no theoretical meaning..(I guess this is happening because of a crossover design and sample size).. The question is, can I "ignore" this irrelevant interactions and look at the main effect only? Thank you!! ... View more