The following is a recurrent issue in our study and by now no consensus have been reached in my team. We made our subjects to perform some neuropsychological tests. An italian validation sample is availlable for all of them and their manuals provide instructions to correct the raw scores accordingly (stratified by: age, gender, and schooling).
In our studies, we inserted the corrected scores in a regression model as independent variables, but we decided not to insert also age, gender and schooling as covariates. Considering the previous correction process, we thought that the confounding effect of these variables has already been controlled for and there is no need to do it in the regression model. Inserting age, gender and schooling would result in no further correction (at the expense of an increase in the number of predictors) or even in a possible "overcorrection" in some situations.
However, some others point doubts on this, saying that the insertion of the covariates in the model is anyhow necessary.
What do you think is the most correct procedure?
You need the covariates for avoiding effects of age, gender and schooling. But you must check the collinearity between variables. Every time that you do regression analysis with multiple variables it is interesting to check the correlation matrix and use stepwise algorithms (for Bayesian or machine learning algorithms). It is the best way to avoid problems with collinearity
So, my advice is
1.- Check the correlation matrix
2- Do an stepwise
3.- Use the lower BIC instead of "R square" for choose the model for avoid the overstimulation due to excesses factors
Probably you can do everything with SPSS
Nice suggestions to go for BIC instead of R2! And thanks for the reply!
So, do you think that the previous correction according to the validation sample isn’t (theoretically) already providing a correction for the sociodemographic characteristics?
With this process, you change the score of each subject so that it is now positioned at a certain point of the performance distribution of the sub-population of subjects with the same age/gender/schooling characteristics. Thus, their corrected scores indicate their performance taken into account their age/gender/schooling characteristics.
It may remain a relationship between age/gender/schooling and the dependent variable (neuropsychological tests scores were the independent ones) but in this case the insertion of a covariate it should not be necessary (to correct for a confounding effects of a third variable, this one need to be related to both the independent and the dependent variables).
Y
Yes it is a good point. So, I guess that it is important to observe the correlation matrix too check the dependence between variables, the neuropsychological tests and explanatory variables. Anyway, If you have some doubt you can put together in a stepwise process for check this collinearity.
I am really fan to do statistics with strong background in ideas more than by "numeric way", if you believe that to variables and the variable are independent it is better to do the statistics without it. If you are not sure it is better to check this kind of effects, it is possible that two variables are independent but when the variable appears become dependent. If you don't check it you can to have problems with the referee.
Of you now how to use R software you can run this code. And you understand that I mean. I put the results of R console, hence you can check the results (even if the program is not familiar for you)
Good luck and better research. Cheers
#################################################################
set.seed(10) # Fix seed for the random varibles
# Create variables
x1 |t|)
# (Intercept) 1.29398 2.09137 0.619 0.537547
# x1 1.99993 0.02083 96.000 < 2e-16 ***
# x2 0.72901 0.20226 3.604 0.000496 ***
# ---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
# Residual standard error: 0.9739 on 97 degrees of freedom
# Multiple R-squared: 0.9896, Adjusted R-squared: 0.9894
# F-statistic: 4610 on 2 and 97 DF, p-value: < 2.2e-16
#
#
# > BIC(mod)
# [1] 293.8658
#
# > # Other models
# > summary(lm( y ~ x1))
#
# Call:
# lm(formula = y ~ x1)
#
# Residuals:
# Min 1Q Median 3Q Max
# -3.1596 -0.6223 0.1859 0.7493 2.6301
#
# Coefficients:
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 2.42117 2.19071 1.105 0.272
# x1 1.99557 0.02203 90.571 BIC(lm( y ~ x1))
# [1] 301.8295
#
# > # X2 it is idenpendet
# > summary(lm( y ~ x2))
#
# Call:
# lm(formula = y ~ x2)
#
# Residuals:
# Min 1Q Median 3Q Max
# -20.9307 -6.9010 -0.0086 6.8308 23.5475
#
# Coefficients:
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 200.9947 2.1016 95.641 BIC(lm( y ~ x2))
# [1] 745.7054
#
# > # Correlation matrix
# > cor(cbind(y, x1, x2))
# y x1 x2
# y 1.00000000 0.99407964 -0.02041253
# x1 0.99407964 1.00000000 -0.05803451
# x2 -0.02041253 -0.05803451 1.00000000
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