Linear Regression with ordinal dependent variable

[Santiago Rodrigo Frasseren]

Hello comunnity.

I have a survey database of individuals of 4 different countries. I would like to perform an OLS regression where I have 7 different dependent variable which are ordinal. First group of 4 dependent variables have a range from 1 to 9 and measure how individuals agree with some statement. For instance, first statament says "Politicians should reduce their salary in time of crisis", and respondents must choose how much they agree with that statement, where 1 means "strongly desagree" and 8 means "strongly agree". The others 3 dependent variable are similar and have a range from 1 to 3 and try to measure potential reactions of the respondents in different hyphotetical situations. More specifically, imagine that you can save a person from being run over by a car. Answer one says "I would never put in risk my life", option 2 says "I would only intervene if the car is far enough" and 3 says "I would always try to save the person". This potential reactions are operationalized in that three different answers and have numbers from 1 to 3 in the dataset. Please, let me know if this explanation is not crystal clear for you.

I have a set of covariates which describe the context of each respondant, but I alsove have a set of independent variables which are of main interest. Specifically, this variables are some interval, and others are also ordinal. For instance, one group of four variables ranges from 1 to 3 and meaures some personal traits of respondents (for instance "how honest do you think you are?", and possible answers "1: a lot, 2: some, 3 a little").

I know that maybe the best option here is to perform an ordered logit or probit since using a linear regression here would be violating essential assumptions of the OLS. However, let's consider here that this is trivial in practice and assume that OLS is a good option (I have already performed Logit and Probit estimates and results are consistent). My questions regard to how best interpret the results of the model:

• Which should be the best way to interpret coefficients here of my main independent variables?
• Should I consider the coefficients as changes in probabily like a binary dependent variable linear model?
• Should I consider the first group of dependent variables, which ranges from 1 to 9, as continuous?

Here I provide an example of the output:

	Dep1	Dep2	Dep3	Dep4	Dep5	Dep6	Dep7
Inverval1	0.00	0.02**	0.01**	0.01	0.00	0.00	0.00
	(0.00)	(0.01)	(0.01)	(0.01)	(0.00)	(0.00)	(0.00)
Ordinal1	0.28	0.28	0.23	0.32	-0.34***	-0.09	-0.06
	(0.20)	(0.20)	(0.24)	(0.27)	(0.12)	(0.13)	(0.09)
Ordinal2	-0.08	-0.09	-0.08	-0.19	-0.12*	-0.07	-0.06
	(0.09)	(0.09)	(0.11)	(0.13)	(0.07)	(0.07)	(0.04)
Ordinal3	-0.05	-0.05	0.03	0.05	0.04	0.10	0.06
	(0.09)	(0.09)	(0.11)	(0.13)	(0.07)	(0.07)	(0.05)
Ordinal4	-0.18**	-0.19**	-0.32***	-0.43***	-0.09*	-0.13***	-0.06*
	(0.07)	(0.07)	(0.09)	(0.09)	(0.05)	(0.05)	(0.03)
Inverval2		-0.02	-0.07**	-0.03	-0.02	-0.04*	-0.02
		(0.03)	(0.03)	(0.03)	(0.02)	(0.02)	(0.01)
Constant	4.80***	4.88***	6.23***	3.89***	2.99***	2.19***	1.95***
	(0.53)	(0.53)	(0.61)	(0.74)	(0.42)	(0.40)	(0.25)
Observations	4391	4391	4391	4391	4391	4391	4391
R-squared	0.081	0.080	0.063	0.078	0.077	0.083	0.058
Country Fixed Effects	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Year	2015	2015	2015	2015	2015	2015	2015

Inverval 1 and Interval 2 are the interval independent vars and Ordinal1 to Ordinal 4 are the ordinal independent variables which range from 1 to 3. Dep1 to Dep4 range from 1 to 9. Dep5 to Dep9 range from 1 to 3.

Thank very much to all.

Warm regards.

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of useful answer by following the FAQ on asking questions-provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

You interpret the coefficients just the way you would in any other regression. A one unit increase in the right hand side variable increases the predicted dependent variable by whatever the coefficient is. So, a one unit increase in ordinal for results in a .18 reduction in predictive value for dependent variable one.

[Richard Williams]

I agree with Phil and will add a few things.

This handout offers suggestions for handling ordinal independent variables:

https://www3.nd.edu/~rwilliam/xsoc73...ndependent.pdf

As far as ordinal dependent variables, yes, if you use OLS you are treating them as continuous. Thar might not bother me so much with an ordinal variable that has 9 values but it would make me nervous if the DV only has 3 possible values.

[Santiago Rodrigo Frasseren]

Thank you both. Another feasible option is to transform the ordinal variable into a binary one, so as one can work like in the Linear Probability Model. Regards.