sem + estat teffects command lead to no path/ constrained

[Robin Klomp]

Hello,

I am trying to run a mediation model with Stata with observed variables. I have panel data based on firm and year.
These are the variables I am trying to run the mediation analysis with: X: InvestorPressureScore; M: EnvironmentalPillarScore; Y: ROA1
First, I run the sem command and get results. To be able to interpret them, I tried running

estat

teffects

This is where the issues start. Stata says (no path) or (constrained) and does not give me z-value, p-value or a confidence interval.

It would be great if someone could help me figure out the error!

Thank you,
Robin

. sem (EnvironmentalPillarScore		EnvironmentalPillarScore	InvestorP
> ressureScore), nocapslatent
(1371 observations with missing values excluded)
Endogenous variables
Observed: EnvironmentalPillarScore ROA1
Exogenous variables
Observed: InvestorPressureScore
Fitting target model:
Iteration 0: log likelihood = -94727.46
Iteration 1: log likelihood = -94727.46
Structural equation model Number	of	obs = 3,795
Estimation method: ml
Log likelihood = -94727.46

OIM
Coefficient std. err.	z	P>z	[95% conf.	interval]
Structural
EnvironmentalPillarScore
InvestorPressureScore 7.61e-09 8.18e-10	9.30	0.000	6.01e-09	9.21e-09
_cons 48.99126 .4525535	108.26	0.000	48.10427	49.87824
ROA1
EnvironmentalPillarScore -.0000661 .0000438	-1.51	0.131	.0001519	.0000197
InvestorPressureScore 8.61e-13 2.23e-12	0.39	0.699	3.51e-12	5.23e-12
_cons .0717931 .0024672	29.10	0.000	.0669574	.0766287
var(e.EnvironmentalPillarScore) 695.4355 15.96489		664.8384	727.4407
var(e.ROA1) .005056 .0001161		.0048336	.0052887
Note: The LR test of model vs. saturated is not reported	because	the fitted
model is not full rank.
.
end of do-file

. estat teffects
Direct effects
	OIM
Coefficient	std. err.	z	P>z	[95% conf.	interval]
Structural
EnvironmentalPillarScore
InvestorPressureScore	7.61e-09	8.18e-10	9.30	0.000	6.01e-09	9.21e-09
ROA1
EnvironmentalPillarScore	-.0000661	.0000438	1.51	0.131	-.0001519	.0000197
InvestorPressureScore	8.61e-13	2.23e-12	0.39	0.699	-3.51e-12	5.23e-12
Indirect effects
	OIM
Coefficient	std. err.	z	P>z	[95% conf.	interval]
Structural
EnvironmentalPillarScore
InvestorPressureScore	0	(no path)
ROA1
EnvironmentalPillarScore	0	(no path)
InvestorPressureScore	-5.03e-13	(constrained)
Total effects
	OIM
Coefficient	std. err.	z	P>z	[95% conf.	interval]
Structural
EnvironmentalPillarScore
InvestorPressureScore	7.61e-09	(constrained)
ROA1
EnvironmentalPillarScore	-.0000661	.0000438	1.51	0.131	-.0001519	.0000197
InvestorPressureScore	3.58e-13	(constrained)

[Clyde Schechter]

Your post is difficult to read. To get the -sem- output more readably displayed, post it between code delimiters. (Use the # button on top of the edit wiindow to create a pair of code delimiters.)

More important, we cannot see the actual exact command you gave, and without that it is impossible to fully understand the output. Please post that (also between code delimiters) for further advice.

[Robin Klomp]

Hey Clyde,

sorry about that and thanks for the tips - I hope it becomes more clear now.

As I mentioned, I would like to run a mediation model with the following variables:
Independent: InvestorPressureScore
Mediator: EnvironmentalPillarScore
Dependent: ROA1

First, I use

sem (EnvironmentalPillarScore <- InvestorPressureScore) (ROA1 <- EnvironmentalPillarScore InvestorPressureScore), nocapslatent

and it works fine.

Then, I would like to test whether the effects are significant and use

estat teffects

This is where the problem starts setting in. Instead of the p-value, Stata tells me 'no path' and 'constrained' for the indirect effects and total effects.

Do you know what could possibly be causing this?

Thank you,
Robin

[Clyde Schechter]

OK. This is much better.

As far as the (no path) results, these are correct. There is no indirect path from EnvironmentalPillarScore to ROA1, nor from from InvestorPressureScore to EnvironmentalPillarScore. Only direct paths between those variables are specified in your model.

I do not really know why the indirect and total paths from InvestorPressureScore to ROA1 are said to be constrained. But I have a hunch. The direct paths emanating from InvestorPressureScore to EnvironmentalPillarScore and ROA1 have very small coefficients and extremely small standard errors. My guess is that when the indirect effects are calculated, the resulting standard error is so small that it falls below some threshold which Stata considers to be 0. All of Stata's estimation commands encounter numerical difficulties when there are extremes of scaling in the same model, and I suspect this is what is happening here.

If my guess is correct, you can fix this by rescaling. I have no idea what the InvestorPressureScore is, nor what units it is measured in. But I think if you rescale it downward, say by a factor of 10⁶ or 10⁹, you will get the inferential statistics you are currently missing. If the score is measured, say, in dollars, then this is equivalent to simply denominating it in units of millions of dollars instead. If that doesn't work I don't know what else might be going on. But it certainly can't hurt to try.

[Robin Klomp]

Dear Clyde,

thank you for clarifying and offering your insights.

Perhaps to facilitate the understanding, the Investor Pressure Score measures the number of sustainability keywords on institutional investor sites multiplied by the number of shares the investors own. To get the data on a firm level, all institutional investor scores are cumulated per firm. The mean score is 186,035,746.

As you suggested, I tried rescaling, however, it did not work as expected. I considered another possibility. This would be to transform the above mentioned variables to ln:

gen ln_InvestorPressureScore = ln(InvestorPressureScore)
gen ln_EnvironmentalPillarScore = ln(EnvironmentalPillarScore)
gen ln_ROA1 = ln(ROA1)

Ln worked and the data was no longer constrained in the Total Effects model. However, a friend made me aware that I cannot take the ln of 0. In my 5,166 total observations, I have 38 occurrences of 0. As I explained the measure of the Investor Pressure Score, these are important to get proper results. My friend suggested calculating the score +1 everywhere and then taking the ln. However, after reading multiple reviews online, I am now unsure whether this is a reasonable thing to do.

It would be great if you could give me your take on this matter and whether you think this could be used as an equivalent to rescaling, as you suggested.

Kind regards,
Robin

[Clyde Schechter]

The +1 kludge with logarithms of variables that can be zero is one I dislike intensely. Some others do find it acceptable. My objection is that the 1 is arbitrary. To avoid zeroes one could also look at log(x+1000) or log(x+0.0000001). And the problem is that the results you would get with these different choices of the offset can be dramatically different.

You might consider other transformations that compress the range of the data, such as the square root or cube root. But before doing any of that, have you graphed the data to see what kind of relationships we are really dealing with? In particular, what can you see about the behavior of the ROA1:Investor Pressure Score relationship when the latter is 0 or close to 0. It may be that the zero-observations are really qualitatively different from the non-zero ones and don't belong in the same model. Or it may be that there is flat relationship among low values, including 0, which then "takes off" beyond some threshold.

Another thought would be to revise the definition of Investor Pressure Score, if it is not a measure that is already established and widely used. I suspect that much of the variation in this score comes from the number of shares owned. And I would bet that all of the zeroes come from zero keywords, not from zero shares owned. So maybe a better definition of this score would be to multiply the number of keywords by the logarithm of the number of shares.