In my data set the dependant variable is a percentage with a range 0 to 100. It can be interpreted as the probability or proportion as well. Ex:- Number of correct answers provided by the respondents out of 14 questions in a questionnaire. Data set shows an approximately normal distribution but the normality test is significant. Can I use multiple linier regression to analyze this kind of data set?
Be careful with percentages. They must be percentages of the total. The percentage of A/B is non-linear. The percentage of A/(A+B) is linear.
Hi,
Sure you can. A dependent variable in linear regression has to be quantitative and normally distributed. Your examples fit the first demand. If your variable is not normally distributed, you can either try to "normalize" it using transformations (i.e., Log) or try to fit other type of regression (for ex: Poisson if you have count data with right-sqewed distribution).
Be careful with percentages. They must be percentages of the total. The percentage of A/B is non-linear. The percentage of A/(A+B) is linear.
I agree with Joseph. Percentage is ratio or proportion in decimal multiplied by 100. Part over whole times 100 is percentage. Part over part times 100 is also percentage.
Hi Suchira. I totally agree with both Marina and Joseph. Taking into account Joseph's commentary you can assume your variable to be continuous and as Marina says, you must check for linear regression assumptions (normality, homocedasticity, absence of residuals' serial correlations, etc). Be aware that your model may, in certain conditions, predict negative percentages or even percentages above 100% and this will problaby be absurde. I don't know the specifics of your study but if possible you should consider logistic regression as it obviates the later problem.
Hope it helps!
Yes, Suchrira, percents are continuous, so general linear models are appropriate. If you variable is not normally distributed (after applying the appropriate statistical test for normality) then you can consider categorizing the outcome into something that is clinically significant. For example, passing or failing would be binary and logistic regression could be used. If you wanted more than two categories, you could use ordinal regression. For example the dependent could be above average, average, below average ( the median or mean could be used).
Suchira I agree with Goroshit. Also explore use of non-parametric statistical method not affected by mormality.
Sure, I also agree with the use of linear regression models since percentages are continuous. But the caution pointed by Joseph has to be taken care of.
Sucheria, would you please provide us with more details of your study? It is important to understand the clinical significance of the percent responses. If there is a certain requirement for recommended or average, then it is possible to use logistic regression. I think that a pass/fail method can work when you want to adjust for confounders such as age, gender, race/ethnicity, biomarkers...etc
Dear Friends,
Thank you very much for your valuable answers and kind contribution. I am trying to identify factors affecting knowledge on abortion. My DV abortion Knowledge were measured using 14 questions and developed a scale. E:- Percentage of correct answers.
So, Can I use multiple linear regression to analys this?
What are the components of regression? Is it possible to perform simple regression on the separate components? Do you know how the components interact?
In principle you may use linear regression with your data if your scale is continous and the bounds don't seem relevant (means: not many observations at the maxima, no strong bounding effects in residuals vs. predicted values).
As far as you have described it so far distributional assumptions seem to apply.
Though your DV may in principle considered to be continous, it is bossible that the mapping of knowledge (latent variable) to average of answers (observed indicator) is not linear. This would lead to problems with the interpretation of the regression results. It is advisable to check if your scale fullfills rasch properties to be on the safe side.
Consider transforming the response variable to normal scores or quantiles.
SAS: http://support.sas.com/documentation/cdl/en/proc/61895/HTML/default/viewer.htm#a000146840.htm
SPSS: http://www.psychstat.missouristate.edu/introbook/sbk14m.htm
STATA: http://www.ats.ucla.edu/stat/stata/faq/prank.htm
Dear Courageous,
Greetings from Sri Lanka
Thank you very much for your valuable feedback and recommendations. I would like to share the outputs of few models which I have developed using your recommendations and feedback. There are four models;
DV as a
1) Total Number of questions correctly answered by the respondents – Multiple linier
2) Proportion / Percentage of questions correctly answered – Multiple linier
3) Categorical – Ordinal (Categories; 1=bellow Q1, 2=Q1 to Q3, 3= Above Q3)
4) Categorical – Multinomial logit (Categories; 1=bellow Q1, 2=Q1 to Q3, 3= Above Q3)
Could you please review the outputs and kindly share your feedback. What is the best fitted model for my data?
Thanks a lot,
Warm Regards,
Suchira
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