How did you get different multiple correlation values R in your multivariate analysis?

What do you mean by performing a correlation in a multivariate manner?

The attached article may be helpful. It can also be downloaded here: http://www.personality-project.org/r/book/chapter5.pdf

The print out that you attached appears not to be accurate to lump correlation coefficients together in one column. These factors: Age, sex & smoking are non-quantitative data. The r here should come from biserial-type of correlation. They need to be looked at separately because in regression, these factors required logit or probit, not OLS linear regression. Other factors could have been quantitative and correlation would have been calculated under Pearson r. They should be treated separately because the regression model here (in single factor) is a straight forward linear regression: Y = a + bX.

On the multi-variate column, it appears the print out is a reading of linear-relationship measurements in a form of X1 to Y, X2 to Y, X3 to Y, etc. as evidenced by 4 separate reading of R. See attached Chapter 5 to double check the value by manual calculation according to the equations provided therein. R here would be one value for one multi-variate model.

To bi-pass all the above for multivariate testing, you might consider F test in ANOVA: F = MSR / MSE. This will allow you to evaluate whether the proposed multiple variable regression model could explain the data.

@mehmat

That is thing i need to ask, in simple bivariate correlation we just correlate two variables in simple manner. But I need to ask if we want to see correlation between more than two variables then what will we do. For example, we want to see correlation between serum creatinine and other variables like age, gender, BMI, comorbidities (hypertension and diabetese). Then how can we calculate by SPSS?

@paul

Thank you so much for your eloborative answer

I think you belonged to statistical field and provided much complex document that is very difficult for medical students like me (hehehe). Any how thank you so much. Actually in our field we can just perform analysis by using SPSS and have little bit knowledge of background statistics. We totally rely on out data file of spss and just interpret it according to our need.

Can you please guide us is simple manner, as I gave answer to Mr Mehmant above

When SPSS print out r values for each independent variables (factors 1, 2, 3, ..), it means that it perform correlation coefficient calculation for each factor, i.e. reporting linear relationship of each IV (X) to DV (Y). Your editor may have raised a point: "if you ran multiple regression for your proposed model, what was your measure of the relationship? or how much does your proposed model explain the data?"---The answer to this question may be found in the article I attached above on page 130; to wit I quote:

"If the predictor set xi,xj are uncorrelated, then each separate variable makes a unique contribution to the dependent variable, y, and R2,the amount of variance accounted for in y, is the sum of the individual r2." The author gave the formula for R-squared:

R2 = ΣBirxiy

With your print out you have now, you have the separate rxiy part of the equation. Find Bi and multiply then sum them to get R2. How to find Bi? This is explain on page 128 as:

B1 = rx1y - rx1x2B2

B2 = rx2y -rx1x2B1

In your case you may have up to 6 factors: (x1, x2, x3, x4, x5, x6). Just repeat the above factor crossing calculation for all 6 factors.

Diabetes mellitus

Cardiovascular disease

Hyperlipidaemia

Fluid overload (OH)

Proteinuria

Diuretics

The interpretation is stated on page 129: "The βi are the direct effects of the xi on y. The total effects of xi on y are the correlations, the indirect effects reflect the product of the correlations between the predictor variables and the direct effects of each predictor variable."

You have rxiy in your print out. You are missing rx1x2. you can tell SPSS to do it or use simple excel command in MS Excel: =CORREL(array1,array2).

I hope this is helpful. Cheers.

Tauqeer

First of all not everything is about correlation. I mean you need not find correlation for every analysis. There are other methods like regression.

If you wish to stick to correlation then there are alternatives. Semi partial and partial correlations are applicable for your case. What these two do is take the effects of other variables controlled and then calculate the correlation between two. What I mean is let's say we have variables x,y,z,t and we wish to calculate correlation between x&y while controlling the effects of z&t. Here you can use semi partial or partial correlation. In semi partial correlation, you remove (control) the effects of z&t from only x or y. In partial correlation you remove effects of z&t from both x&y.

One more correlation is multiple correlation coefficient and it is related to regression.It is the correlation between predictors x,z,t and dependent variable y. See below. I supposed you calculated this coefficient in your multivariate analysis. But it must be unique (to a dependent variable and remaining predictors) while you have many different values.

There is also canonical correlation which is related but might be beyond the scope of your analysis.

In regression, you do a similar job like partial correlations. But an important difference is you should have a dependent variable say y. For correlations you might have also a dependent variable but it is not a must. In regression you find the effects of x,z,t on y. When you do regression you also control effects. Regression might be preferred.

Paul,

Thank you so much for your time and guidance in this matter. I am now reading full document attached by you.

In case of any confusion i will come back to you.

Mehmat

Thank you for your reply and guidance in my matter. I think I made some confusing point in print out that I attached. Now I am getting your point.

PLEASE CORRECT ME if i am wrong, I got following point

Glomerular filtration rate (GFR) is dependent variable

Diabetes mellitus

Cardiovascular disease

Hyperlipidaemia

Fluid overload (OH)

Proteinuria

Diuretics

above all are independent variables.

1. In univariate, first I have to do bivariate correlation of each IV with DV like Diabetese mellitus and GFR, Cardiovascular disease and GFR,......... diuretics and GFR. By this manner I will get r values for each independent variable and I can calculate r2 value by just multiplying of r with r for each variable. So after doing this by spss, i will get r, r2 and p value of each IV that will tell us their correlation with DV (GFR).

2. Based upon your suggestion, If i want to see r values by controlling confounders then I need to do partial correlation and in this partial correlation I will again put two variables in "variables box" and confounders in "controlling for" box, now i will again get r, r2 and p value for IV after controlling some confounders.

These are major two points that I understood from your above message.

Ok now I have some questions here, in both univariate and partial correlation, we are putting one IV1 with DV (GFR) and get results then again we perform same procedure for IV2 and then again for IV3 and so on...... I just want to ask one thing that can we put all independent variables along with dependent variable in "variable box" and if we can do so then is it multivariate analysis?

Second question is, in linear regression we put all the variables in IV box and GFR in DV box, then in output file we just get one R2 value along with adjusted R2. Is this R2 is for all IV used in analysis? can we get indivisual R2 for each IV in linear regression? and how can we calculate incremental R2?

I hope now you can understand that what I want to do? Please if you dont understand please tell me I will first tell you about my data and then ask you that what I want to do

"can we put all independent variables along with dependent variable in "variable box" and if we can do so then is it multivariate analysis"

If I understand correctly, you will put all variables into bivariate correlation variable box then compute pairwise correlations. If so, then this would not be a multivariable analysis (multivariate is a wrong term to be used in this case).

" Is this R2 is for all IV used in analysis?"

Yes, this R squared will be the multiple correlation coefficient.

" can we get indivisual R2 for each IV in linear regression?"

Yes, and this would not be different from the one you obtain from squaring the bivariate correlation of x&y using bivariate menu.

"how can we calculate incremental R2?"

You can calculate incremental R2 manually, or by a stepwise procedure.You see there are options in SPSS regression menu like "Enter,forward, backward etc."

I understand what you wanted to do.

Mehmat

Thank you so much. Now I got your point. Please just help me in one matter

In bivariate correlation we get value of r and then we multiply this value with 2 and we get R2 for each variable

In linear regression, we get value of R2, that is actually value of all variables (model).

In linear regression, we also get another coefficient that is unstandardized or standardized beta coefficients of each variable? what is this coefficient? is it same as r that we get in bivariate correlation? and how can we interpret values of beta coefficient? will it be interpreted by same manner as we do for correlation coefficient r?

I found one way to calculate incremental R2, for example if i have x dependent variable and Y1, Y2, Y3 as independent variables, Then if i put Y1 in block 1, then Y1, Y2 in block 2, then Y1, Y2,Y3 in block 3 and so on. Then we can get R2 for each block that will be higher from preceding block. For example In block 1 model we will get R2 for Y1 and in block 2 we will have separate R2 for both Y1 and Y2, so we can substract R2 value of Block 2 from block one, that will incremental R2 of Y2 variable. E.g. R2 of block 1 (having Y1 only) minus R2 of block 2 (having Y1 and Y2 both) = Incremental R2 of Y2. WHAT YOU SAY ABOUT THIS METHOD?

Can we say that value of R2  in linear regression is mean of values of R2 obtained by bivariate correlation of each variable?

Which R2 from linear regression we should use? either unadjusted or adjusted R2?

How can we control confounders in linear regression? as in partial correlation we have an box of "controlling for" but how to deal with confounders in linear reg?

If one of my variable is highly correlated in bivariate correlation with dependent variable but in linear regression it had p value >0.05, so in this case should i take conclusive decision that this variable is not correlated with dependent variable?

Brother, I am sorry, I know that I am bothering you a lot here, But if you have difficult to manage reply, It will be ok. I can understand the workload of researchers. THANK YOU SO MUCH FOR YOUR CONTINUOUS HELP AND GUIDANCE.

There are numerous questions. I will give short answers. I suggest consulting a textbook or another source.

(Un)standardized regression coefficients are not correlations but they are related to correlation coefficients. Regression coefficients are interpreted like this, a one unit increment in the corresponding predictor will cause an increase/decrease in the dependent variable as much as the value of unstandardized regression coefficient while holding the other predictors fixed. They are not interpreted like correlations.

You can find incremental R^2 changes like you proposed. R^2 in regression is a linear combination of bivariate correlations,actually it is a weighted sum of those correlations where weights are standardized regression coefficients. R^{2}= \sum\beta _{i}r _{Yi}

You can use both. For model selection purposes adjusted R^2 is preferred.

You can control confounders by inserting them into model.

P values might be deceiving. Predictors might have high correlations alone but low correlations when together with others. This is also about confounding.

Mehmat

Really appreciated. Thanks a lot for your answer

Tauqeer I suggest you go through this article, its not directly answering your question but it may add a different perspective on what your trying to find out...

http://blog.minitab.com/blog/adventures-in-statistics/how-high-should-r-squared-be-in-regression-analysis

According to which investigating R2 in a model becomes irrelevant when you are only looking for a correlation between IV and DV. If your reviewer is asking for it, then he is asking to check how precise is the prediction accuracy of your model, which is still not the right choice as R2 does not provide the answer that how much the predictions are precise enough to your needs. For this purpose you must use prediction intervals, which is how short is your 95% CI. 

Quotationsfrom the article below:

"If your main goal is to determine which predictors are statistically significant and how changes in the predictors relate to changes in the response variable, R-squared is almost totally irrelevant."

"If you correctly specify a regression model, the R-squared value doesn’t affect how you interpret the relationship between the predictors and response variable one bit."

"A low R-squared doesn’t negate a significant predictor or change the meaning of its coefficient. R-squared is simply whatever value it is, and it doesn’t need to be any particular value to allow for a valid interpretation."

"In order to trust your interpretation, which questions should you ask instead?

Is there a sound rationale for my model and do the results fit theory?

Can I trust my data?

Do the residual plots and other assumptions look good?

How do I interpret the p-values and regression coefficients?"

"If your main goal is to produce precise predictions, R-squared becomes a concern. Predictions aren’t as simple as a single predicted value because they include a margin of error; more precise predictions have less error."

"R-squared enters the picture because a lower R-squared indicates that the model has more error. Thus, a low R-squared can warn of imprecise predictions. However, you can’t use R-squared to determine whether the predictions are precise enough for your needs.

That’s why “How high should R-squared be?” is still not the correct question.

Which questions should you ask? In addition to the questions above, you should ask:

Are the prediction intervals precise enough for my requirements?"

"R-squared gets a lot of attention. I think that’s because it appears to be a simple and intuitive statistic. I’d argue that it’s neither; however, that’s not to say that R-squared isn’t useful at all. For instance, if you perform a study and notice that similar studies generally obtain a notably higher or lower R-squared, it would behoove you to investigate why yours is different."

Article by Jim Frost

-a technical writer at Minitab-

Dr Omaid Hayat Khan

Thank you for your detailed answer, I read the link and found some relevant information that was required.

I will discuss with you soon