# Semi-Parital (Part) Correlations

#### edieb

##### Senior Member
10+ Year Member
Hey, I am trying to crunch data and have a question: Is is reasonable to perform a semi-partial correlation on each item in my newly devised instrument to see which items correlate with my d.v. and then take the items that correlate well with my d.v. (positively and negatively) and put them together and perform an internal consistency analysis to try to put them together in an instrument?

This seems to me to have the same underlying logic of a Exploratory factor analysis?????

#### psychgeek

##### Senior Member
10+ Year Member
7+ Year Member
edieb said:
Hey, I am trying to crunch data and have a question: Is is reasonable to perform a semi-partial correlation on each item in my newly devised instrument to see which items correlate with my d.v. and then take the items that correlate well with my d.v. (positively and negatively) and put them together and perform an internal consistency analysis to try to put them together in an instrument?

This seems to me to have the same underlying logic of a Exploratory factor analysis?????

Hi there,

Depending upon the candidate predictors, using the semi-partial r2 could pose some issues. Since relying entirely upon sr2 will remove from consideration any variation that can be explained by more than one of the predictors, you might end up with a less than optimal set of items in the final instrument. Selection will be biased toward including those items that are highly dissimilar to other items yet still associated with the predicted variable.

I feel like the above comment is pretty confusing, so I will try to make it more clear with an example. Lets pretend you are trying to predict income from a set of four variables: years of education, parents SES, spouses SES, and age. Though the first three variables will explain most of the variance in the dependent variable, the final variable (age) may have the largest sr2. This is because the other three are likely to be highly correlated with one another and therefore little of the variance they explain will be unique to each individual predictor. Age, on the other hand, is weakly predictive of income but uncorrelated with the other three variables. Thus, almost all of the relatively modest amount of variance it explains will be reflected in its semi partial r2 since it is unique to this variable.

I can certainly see why some consideration of sr2 is attractive particularly if you are trying to make a brief instrument. Maybe you could try a sort of balanced approach like stepwise (or preferably hierarchical) regression. This could reduce the total number of items you have in the instrument while minimizing the problem detailed above.

Good luck

OP
E

#### edieb

##### Senior Member
10+ Year Member
thanks for the answer- but now i am thinking semipartial correlation isn't apt for test construction because one test item would never be falsely correlating with the dep variable because, unlike social research, there are no mediating or moderating items in test test construction that could lead to false correlations -- an item is either correlated with the dv or it is not...right

thanks

psychgeek said:
Hi there,

Depending upon the candidate predictors, using the semi-partial r2 could pose some issues. Since relying entirely upon sr2 will remove from consideration any variation that can be explained by more than one of the predictors, you might end up with a less than optimal set of items in the final instrument. Selection will be biased toward including those items that are highly dissimilar to other items yet still associated with the predicted variable.

I feel like the above comment is pretty confusing, so I will try to make it more clear with an example. Lets pretend you are trying to predict income from a set of four variables: years of education, parents SES, spouses SES, and age. Though the first three variables will explain most of the variance in the dependent variable, the final variable (age) may have the largest sr2. This is because the other three are likely to be highly correlated with one another and therefore little of the variance they explain will be unique to each individual predictor. Age, on the other hand, is weakly predictive of income but uncorrelated with the other three variables. Thus, almost all of the relatively modest amount of variance it explains will be reflected in its semi partial r2 since it is unique to this variable.

I can certainly see why some consideration of sr2 is attractive particularly if you are trying to make a brief instrument. Maybe you could try a sort of balanced approach like stepwise (or preferably hierarchical) regression. This could reduce the total number of items you have in the instrument while minimizing the problem detailed above.

Good luck

#### psychgeek

##### Senior Member
10+ Year Member
7+ Year Member
edieb said:
thanks for the answer- but now i am thinking semipartial correlation isn't apt for test construction because one test item would never be falsely correlating with the dep variable because, unlike social research, there are no mediating or moderating items in test test construction that could lead to false correlations -- an item is either correlated with the dv or it is not...right

thanks
depending on the number of items there could be issues with suppressor effects and multicolinearity still poses a problem. On the other hand, if you used simple zero-order pearson correlations instead of multiple regression this won't be an issue. However, this could result in a measure riddled with items that are largely redundant.

I'd use the zero-order approach or hierarchical multiple regression myself.

Good luck