FAQ: unidimensional vs. multidimensional variables
Q: Is my dependent variable unidimensional or multidimensional?
A: First of all, if a variable is measured with a single question on a questionnaire, it's always unidimensional. Multiple questions on a questionnaire can be either unidimensional or multidimensional -- just because there are multiple questions doesn't mean that the variable must be multidimensional.
The reason you'd put multiple questions on a questionnaire is for triangulation of measurement, because any single question might lead to weird answers, but if you ask about the same thing in different ways, you should get a reasonable response to the questions overall. (It's sort of like why you don't want just one person in your sample -- one person might not adequately represent people's answers.)
In general, a variable is unidimensional when it's narrow, simple, and straightforward, and multidimensional when it's more broad, complex, and abstract. Questions used to measure a unidimensional variable give similar answers to each other, and group together in one group. Questions for a multidimensional variable give similar answers overall, but group together in several subgroups.
E.g., income is a unidimensional variable. You can ask it in a few ways -- e.g., "What was the income you reported last year on your income taxes? ________" and "How much money did your household earn last month: $0-500, $500-1,000, or $1000+?" -- so the measure can be triangulated, but it's still a simple, straightforward variable.
But socioeconomic status is a multidimensional variable, because it includes not only income, but also occupation and education. Overall, people's educational level, occupation, and income are closely related, so answers to SES questions should be similar overall, but answers about education should group together closer with each other than to answers about income & occupation, answers about income should be more similar to each other than to answers about education & occupation, etc. So income is a variable, but it's also one of three (or so) dimensions of a "bigger" variable, socioeconomic status.
The way researchers usually find out whether a variable is uni- or multi-dimensional is by running a statistical test called a "factor analysis," which looks at correlations to show how variables group together. Because you're not expected to run factor analyses, you can basically eyeball your data to see what groups together with what, or you can just guess based on what you know about your variables.