Dear Tauqeer: Perhaps my answer will not address exactly what you are asking.

I would say a couple of basic notions. First (not the most important) you can do whatever you want with your database and a software for statistic analysis. 

But, second, you must have a clear as well as precise idea in mind about what do you expect to obtain from this. At first sight 10 variables without and hypothesis or any kind of hierarchical organization is not sound.

I would advice you to figure out how to state a main association and from then on and following a logical line (both biological and epidemiological sound) hypothesise more variables to introduce in your model, but also epidemiologically sound. The total possible number is not the problem in itself and depends of a variety of factors (the software power, for example) but mainly biological and epidemiological ones. The more variables you introduce in your analysis, the higher the likelihood of poor generability will affect your results.

This is a very "compact" bunch of thoughts about your question. Wish I could help you.

@ Patricio thank you so much for your help. Indeed you always guide me in well manner. I dont know what reviewers exactly want, I just want to know that either there is any limitation of number of variables in multivariate analysis or not? E.g. can we analyze 13 variables in multivariate analysis (binary logistic regression)?

 Respected MARIO sir, thank you so much for your reply. I am using logistic regression by SPSS. Ok I ll try PCA method for reduction of variables. secondly, col linearity point is added benefits to my question. 

Can you please guide me about stepwise selection and rejection of variables in logistic regression by Backward, Forward and Enter method?

There is not general answer for such a question.  Apply the method that you want, and when you arrive to a model that fit your data, check the assumptions.

In many cases, it is necessary to solve problems that have many varibles and only a few observations. 

Try to find the simplest model and check that your observations don't contain outliers.

The number of variables is determined by 

1-Theory

2- Review of literature (previous Research) and,

3-Logical basis.

Keep in mind to have at least 30 observations per independent variable. If you have a lot of variables measuring different dimensions then, use Factor analysis as a data reduction technique and use factor scores as independent variables

A reason for avoiding large numbers of predictor variables is that doing so increases the risk that your model will reflect the idiosyncracies of your data set - the model is "overfit" to the data. This harms generalizability. The n/10 rule helps protect your results against this danger.

In general: pick your predictors in advance; pick your predictors to address the literature and your hypothesis; be as parsimonious with your model as you can.

The two main problems are over-fitting and running out of degrees of freedom to estimate the error term - the former being more likely in this case. 

That said, this sort of model could be just fine under some circumstances spending on exactly what you do an the nature of the predictors. The main alternatives are some kind of data reduction method that combines predictors in a sensible way or some kind of analysis that deals with over-fitting (e.g., a Bayesian model with shrinkage).

Dear  Tauqeer,

You have 95 cases not variables. I meant you have 95 observations which represents the sample size (n = 95) , but the variables as age,the degree of urea, ...,etc.

Check it please.

Best Wishes

Hello Tauqeer.  The good points that Thom Baguley raised earlier are discussed in Mike Babyak's very readable article linked below.  Babyak also discusses use of stepwise methods, which someone else mentioned earlier.  I hope this helps (HTH). 

http://www.cs.vu.nl/~eliens/sg/local/theory/overfitting.pdf

EDIT (9-Aug-2021)

The link I gave above for Mike Babyak's article on overfitting is not working for me now. Here a re a couple of other links you can try.

https://people.duke.edu/~mababyak/papers/babyakregression.pdf

Article What You See May Not Be What You Get: A Brief, Nontechnical ...

Dear Tauqeer, there is no limit to the number of variables that can be analyzed by means of multi-(or mega-)variate analysis. The most favorable case is the one in which the number of observations is much higher than the number of variables, but it is not a necessary condition. You should certainly avoid "square" matrices, namely datasets that have about the same number of observations and variables. However, in order to avoid problems of overfitting, in my opinion, the key is to pay particular attention to the predictive validation of the model you have obtained.

At first, you ignore his advice. In the regression and discriminant analysis, I analized 240 cases with 19-independent variable and strong collinearity. If we choose the best model, I can avoid the collinearity and resolve other problems. See my papers about CPD data after 2014.

Dear Tauqeer Hussain Mallhi

First of all ,it is imperative to keep in mind that the number of predictors to be included in the multivariate analysis is determined by:

1- theory

2- previous research and 

logical basis

Knowing that then, we can take the advice of the experts in multivariate analysis such as Kerlinger and Pedhazur who state that we have to use at least 30 cases per independent variable.

Since you have limited number of cases then, it is recommended to use the data reduction technique (Factor Analysis) to obtain few dimensions to be included in your multivariate analysis.

Good luck

Dear Tauqeer Hussain Mallhi

First of all ,it is imperative to keep in mind that the number of predictors to be included in the multivariate analysis is determined by:

1- theory

2- previous research and 

logical basis

Knowing that then, we can take the advice of the experts in multivariate analysis such as Kerlinger and Pedhazur who state that we have to use at least 30 cases per independent variable.

Since you have limited number of cases then, it is recommended to use the data reduction technique (Factor Analysis) to obtain few dimensions to be included in your multivariate analysis.

Good luck

Dear Tauqeer Hussain Mallhi

First of all ,it is imperative to keep in mind that the number of predictors to be included in the multivariate analysis is determined by:

1- theory

2- previous research and 

3- logical basis

Knowing that then, we can take the advice of the experts in multivariate analysis such as Kerlinger and Pedhazur who state that we have to use at least 30 cases per independent variable for the stability of Beta weights.

Since you have limited number of cases then, it is recommended to use the data reduction technique (Factor Analysis) to obtain few dimensions to include in your multivariate analysis.

Good luck

Can I use more than 10 variables for Multivariate Analysis? - ResearchGate. Available from: https://www.researchgate.net/post/Can_I_use_more_than_10_variables_for_Multivariate_Analysis#view=5621c8c65cd9e33dbd8b4593 [accessed Oct 17, 2015].

Tauqueer

Can you provide us with a bit more on the questions you are trying to ask with your data? What hypothesis are you testing? Group differences?

what is the difference between multivariate theory and multivariate analysis?

Many opinions are correct, but it is difficult for beginners of statistics to deal with.

To distinguish between the two groups, if 1 and -1 are given as objective variable values ​​to the 2 group, they are the same as the multiple regression analysis, so include it below.

In general, it is desirable that the explanatory variable p is small for the number of cases n. However, if you do a good selection of variables, you do not have to worry about p's decision from the beginning. You can only consider whether the selected model is correct by statistical quantity of model selection.

Even with high dimensional Microarray data of ｎ (100)

There is a statistical principle that for every 10 samples there needs to be 1 event. So, the number of variables that you will enter into multivariate analysis depends on the number of outcomes of interest (event).

I have had experience analyzing 323 cases with 18 independent (predictor) variables using the regression analysis which brought strong statistically significant association of only 2 factors. It is indeed a fact that multiple regression is a simple and ideal method to control for confounding variables. The most important the choice of independent variables.

Regression with only one dependent and one independent variable normally requires a minimum of 30 observations. A good rule of thumb is to add at least an additional 10 observations for each additional independent variable added to the equation.

The number of independent variables in the equation should be limited by two factors:

- First, the independent variables should be included in the equation only if they are based on the researcher's theory about what factors influence the dependent variable.

- Second, variables that do not contribute very much to explaining the variance in the dependent variable (i.e., to the total R2), should be eliminated.

Many difficulties tend to arise when there are more than five independent variables in a multiple regression equation. One of the most frequent is the problem that two or more of the independent variables are highly correlated to one another. This is called multicollinearity. If a correlation coefficient matrix with all the independent variables indicates correlations of .75 or higher, then there may be a problem with multicollinearity.

When two variables are highly correlated, they are basically measuring the same phenomenon. When one enters into the regression equation, it tends to explain most of the variance in the dependent variable that is related to that phenomenon. This leave little variance to be explained by the second independent variable.

Hi, Malhi

His advice is wrong.

I analysed Cephalo Pelvic disproportion data that consists 240 patients having 19 variables.

See my book "New Theory of Discriminant Analysis after R.Fisher (Springer, 2016.'

Or, you can download my thesis from RG that include CPD.

Now, I developed the first theory of high-dimensional cancer gene data analysis using over 100 microarrays those consist of about 100 patients and over 10,000 variables. See my recent papers from RG.

Tauqeer,

Please specify the question you are asking? Are you comparing the acute cases (95) to the remaining 572 cases or are you asking specific questions about the acute cases? Without more details concerning the questions you are asking no one can answer your question with any degree of certainty.

You can use the Stepwise regression approach to identifying appropriate predictors in your analysis.

My two papers can completely answer these many answers for Malhi's question.

1) Shinmura S (2021a) First Theory of Cancer Gene Data Analysis by 169 Microarrays and Four Universal Data Structures for Big Data

2) Shinmura S (2021b) Twenty-three Serious Mistakes of Cancer Gene Data Analysis since 1995. Transactions on Computational Science & Computational Intelligence, Springer Nature (in Press).

After BIOCOMP'21: July 26-29, 2021, you can download under the HP. Or, you can read two papers from Springer. https://www.american-cse.org/csce2021/conferences-BIOCOMP https://www.american-cse.org/csce2021/

If there are many independent variables, let's say 11 variables! Make sure you include at least 4 variables in a single regression model , and finally you find out running 3 different models! After that, explain the significant variables explaining the dependent variable! In short, we call this as parmonius model!

Including too many variables in a single model or equation leads to parameters overfiting and multicollinearity!

Parmonious model is much preferred to such kind of situation.

If logistic regression discriminates Alon's DNA (64 patients* 2,000 genes), DF of it equals 64. Thus, it can select 64 variables naturally and sets 1936 variables zero.

See my three PPs of the first theory of cancer gene data analysis.

All studies were wrong and useless since 1995.

I've used as many at 120 without a problem.

Sure you can. Depending on variable type, if they are dichotomous, use multiple logistic regression with stepwise to find the most important variable. You can also use PCA and Factor analysis to find interaction of the variables. SAS is a great package to help you analyze that too.