[David Wong]

My prior prejudice is that Tobit is oversold in this context. It's hard to see that in principle that linearity is consistent with bounded responses.

What are the bounds of the outcome in principle (not in practice)? I guess at 13 and 65.

The values seem curiously labile from post to post in this thread? I see 13, 15 and 47, 50.

If so, then I'd rescale to (scale - 13) / 52 (i.e. bounds [0, 1]) and then apply logit link and robust standard errors.

Thank you very much for your good advice, Nick. If changing data from bounded integers into fractions (0,1), should I use fractional response model then? If so, as I am not familiar with the interpretation of coefficients in that model, I will search it.

[David Wong]

If you're concerned, then do some diagnostics, for example, what do the residuals look like?

help diagnostic plots
help regress postestimation plots

Linear regression would seem to be a reasonable option when summing of as many as 13 ordered-categorical items into a Likert scale, unless they're nearly perfectly correlated.

version 14.2

clear *
set more off
set seed 1391759

forvalues i = 1/13 {
local varlist `varlist' y`i'
}
tempname Corr
matrix define `Corr' = J(14, 14, 0.5) + I(14) * 0.5

quietly drawnorm `varlist' x, corr(`Corr') n(100)
foreach var of varlist `varlist' {
generate byte l`var' = 1
forvalues cut = 0.25(0.25)0.75 {
quietly replace l`var' = l`var' + 1 if `var' > invnormal(`cut')
}
}

egen double total = rowtotal(ly?)

histogram total
sleep 1500

regress total c.x
predict double xb, xb

qnorm xb
sleep 1500

pnorm xb
sleep 1500

rvfplot

exit

Thank you so much for your good suggestion and the detailed codes, which is very helpful.