# Factor Analysis

#### noetsi

##### No cake for spunky
I have 27 categories we spend money on. I would like to reduce this to around 8 categories for analysis. I was thinking of using the amount we spent on each of these categories for the covariance. the theory is there are spending dimensions behind the formal categories (like say education).

Is that a legitimate way to do factor analysis?

#### spunky

##### Can't make spagetti
Well, if these are categories we're talking about as opposed to continuous variables, then Multiple Correspondance Analysis would be the correct way to go. But yeah, Factor Analysis or some other dimension-reduction technique would be appropriate. Although, in your case, I'd say Principal Component Analysis is the way to go (again, under the assumption of continuous variables).

#### noetsi

##### No cake for spunky
It is a continuous variable (spending).

I was not sure using spending for covariance is a legitimate way to find factors

I think Principal Component Analysis is one of the ways SAS does FA.

thanks spunky

#### spunky

##### Can't make spagetti
Principal Component Analysis and Factor Analysis are related albeit different methods. In your particular instance, because you're only interested in dimension reduction and not in some mysterious latent variable that accounts for the correlations, Principal Components makes more sense.

Just remember to work with the **correlation** as opposed to the covariance matrix because PCA is sensitive to scaling.

#### j58

##### Active Member
I suspect that noetsi will want to understand what the factors represent in terms of the commodities comprising them, so he'll probably want to do factor analysis. And, yes, I think correlations of spending by individuals among commodities will lead to sensible, understandable factors. The only thing I would caution is that, to my knowledge, there is no way to control the number of factors a factor analysis will produce, so if you want "8 or so" factors, you might not get that number.

#### noetsi

##### No cake for spunky
I will use the various rules of thumb to decide how many factors legitimately load. If its too many that will be an issue, but I doubt it will be. I will have to understand the factors to explain it to those I answer to.

#### ondansetron

##### TS Contributor
It is a continuous variable (spending).

I was not sure using spending for covariance is a legitimate way to find factors

I think Principal Component Analysis is one of the ways SAS does FA.

thanks spunky
As far as I recall, SAS has different methods of PCA and FA since they are different methods with different goals. People often misuse one in place of the other, though, so be careful what you read on this internet!