I have four IVs which measure by 5 Point Likert Scale. The dependent variable is academic achievement which is student market (0-100). Is it any problem for multiple regression?
Hi Mohammad
You can run multiple regression analysis (MRA) with that model. The only concern is, whether your data meets the assumptions and conditions of MRA.
MRA requires the following assumptions/conditions (Saiyidi, Introduction to SPSS, 2014 - see the full text in the link below) :
1. Data type is scale.
2. Number of independent variable (IV) is > 1.
3. Cases to predictors ratio is ‘reasonable’. Sample size, N = 50 + 8(m)Tabachnick and Fidell (2007, p.123), where m = IV.
4. Number of covariates is ‘0’.
5. Linear relationship between variables.
6. Each latent variable is normally distributed.
7. No multicollinearity - check VIF < 10. Ideally VIF < 5.
8. Error variance is assumed to be the same across all values of other variable (Homoscedasticity).
9. no outliers. Multiple regression is sensitive to outliers.
You may want to the publication (link below) for more discussion. Also see:
Allen, P., & Bennett, K. (2010). PASW statistics by SPSS: A practical guide, version 18.0 (1 ed.). Sydney: Cengage Learning Australia Pty Limited.
Best regards
Saiyidi
Article Introduction to SPSS
Technically there is always a problem using likert-type data/likert-scales for tests that assume normality: they can't be normally distributed as they don't even begin to approximate something that resembles continuity. The basis for transforming linguistic data into evenly spaced numerical values is shaky at best (and various studies have shown that response scales which better approximate a continuity or which use fuzzy set theory or other ways to correct for the baseless assumptions behind the Likert-type data transformations). The number of data points is quite low and multiple regression is sensitive to arbitrarily small departures from linearity, normality, and other issues that come up with likert-scales frequently because of the limited number of possible selections (which limits variance as defined by squared deviations, upon which all the standard statistical tests rely). But then, I'm not a fan of multiple regression either, so I'll pretend the two wrongs make a right.
Plot your data. That's probably the most important step you can undertake especiallyin cases like this where responses will cluster (or spread) due to the extremely limited range of the IVs compared to the DV (the DV observations can range over from 0-100 while each IV observation has only 5 possible values). On the one hand, for every observation in an IV, one it's position in space prior to regression is determined by an quinary variable for one coordinate and 101 possible values for the other. On the other hand, depending upon the distribution of the DV observations, this can mean clustering rather than spread. Hence, plot your data (use multiple plots, graphs, whatever helps you "see" the relationship rather than just allow SPSS or some other package to spit out a number).
You can certainly try multiple regression with your data; as Andrew says there are some cautions to keep in mind. You could also do factor analysis which is common for this type of data. Or if you can re-classify your dependent (outcome) variable in to categories, you could do discriminant analysis or even logistic regression if you are familiar with those techniques. But plot your data first to look for outliers as Andrew says. Likert-type tests are notorious for some respondents answering in the extreme (all fives or all ones for example)---you might have to re-classify the Likert-scale answers into categories (yes or no; high or low, etc). This might let you get more useful information from those variables; for example the 'yes' answers might be good predictors but the 'no' answers will not be predictive. And there are often a few subjects who answer in crazy ways and this will make some independent variables less precise in predicting the outcome variable. The statistical significance of each independent variable in your regression will be an indicator of its precision. And two or more of the Likert variables may be highly correlated with each other---you can check this with a bivariate regression plot and correlation. In your analysis you might also want to separately analyze a subset of subjects, for example only those who score high (or low) on the dependent variable, or low (or high) on some of the independent variables. It is common in these analyses to discard some variables because they are collinear with other variables or because they have no predictive value at all in the regression. This usually results in the remaining variables having more predictive power.
Standard regression model (linear) works very well.
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