I'm not 100% sure what you are asking (your research question(s) aren't clear to me), but confirmatory factor analysis (CFA) implies a reflective measurement model where the indicators (measurements, observed variables) are implied to be exchangeable (randomly drawn from the same population of interchangeable indicators of a unidimensional construct). Using variables that are supposed to measure multiple distinct traits as indicators of a single "common" factor violates this principle and probably also would not make a lot of sense substantively (how would you interpret the immune factor?). Rather, I would look at each trait separately. It may not be possible or useful for you to use CFA unless you have multiple measurements (multiple indicators, i.e., at least 2) for each individual trait so that you can specify a separate factor for each trait.

Dear Christian Geiser

Thanks for the reply.

Actually I am looking to define a Latent variable for Immunity System in animal (broilers). These traits have been measured for the research, but the problem here is that some traits are in the humoral immunity class and some are in the cellular immunity class.

Hello Siavash,

this paper could be of interest as it applies CFA/SEM modeling to immunological topics, both discusses implications and problems of a CFA model and comes up with a very creative solution to this problem:

Hayduk, L. A., Pazderka-Robinson, H., Cummings, G. G., Levers, M.-J. D., & Beres, M. A. (2005). Structural equation model testing and the quality of natural killer cell activity measurements. Medical Research Methodology, 5(1), 1-9.

Best,

Holger

Hi Holger Steinmetz

Thank you for your consideration and attention to this matter.

Best,

Siavash

Dear Siavash Manzoori

Factor analysis has a crude statistical concept, therefore when it will apply to immunity assessment you need to develop your biological knowledge deeply.

Although, humoral and cellular immunities follow the same goal as the whole, have different sources of B and T cells and act differently. In my inclination, first, it is better to conduct factor analysis distinctly for each one for feature selection (or identify latent variable) separately for humoral and cellular immunities.

Second: I suggest using group/multiple group factor analysis or even Principal component factor analysis (PCFA).

Third, if it's available, add any other information on white blood cells, hematocrit, antibodies, complement system, lymphatic system, spleen, bone marrow, and thymus as these are the 7 main parts of the immune system.

Fourth, If it's possible divide your samples into two groups of high and low immunity and use artificial neural network analysis+feature selection, then compare selected features from factor analysis and ANN.

Moreover, the following articles can be helpful too:

1- A guide to modern statistical analysis of immunological data

2- Factor Analysis of Clustered Cardiovascular Risks in Adolescence

3- Psychometric validation of the Bangla Fear of COVID-19 Scale: Confirmatory factor analysis and Rasch analysis

All the best.

Dear Peymaneh Davoodi

Thank you very much for your answer and your time.

Best.