SEM and nonlinear regression

[Artyom Mikhaylin]

Hello everyone.

Earlier, I used 'Stata' to build non-linear regressions.
Recently, I started using 'SEM' to solve new problems. I understood a bit the features that I need in 'SEM'. But I do not understand how to do what I did earlier in 'SEM'.

For example
To build a non-linear regression, I enter:
nl( Y = {c}+{x1}*x1+{x2}*x2+{x3}*x3+{x4}*x4)

In SEM :
sem (Y <- x1 x2 x3 x4)

In another case:
nl( Y = {c}+{x1}*ln(x1)+{x2}*sqrt(x2)+{x3}*x3+{x3}*x3*{x4} *x4)

But i don't know how to use 'sqrt', 'ln', and multiplication x3*x4 in SEM.

I read many different articles and topics, tried a lot of command options, but without success. Maybe I missed something or misunderstood, I apologize. But I hope for your help.
Thank you.

[Joro Kolev]

-sem- is a linear system estimator, and -nl- is single equation non-linear estimator. (-nlsur- is a non-linear system estimator.)

-sem- is not able to estimate nonlinear relationships, it is a linear estimator.

[Artyom Mikhaylin]

Joro Kolev Thank you! I assumed this, but some examples using # and others misled me. My misstake.

I need 'SEM' to build models like:
Y= c1 + b11 * x1 + b12 * x2 + b13 * x3 + ...b1N * xN + e1
x1 = c2 + b22 * x2 + b23 * x3 + b2N * xN + e2 (or without const)

Can you tell me which functions I can use for this?

[Joro Kolev]

Joro Kolev Thank you! I assumed this, but some examples using # and others misled me. My misstake.

I need 'SEM' to build models like:
Y= c1 + b11 * x1 + b12 * x2 + b13 * x3 + ...b1N * xN + e1
x1 = c2 + b22 * x2 + b23 * x3 + b2N * xN + e2 (or without const)

Can you tell me which functions I can use for this?

Seems like a standard linear system, so -sem- and -reg3- would both do the job.

And in the equation of x1 you need at least one explanatory variable which is not included in the equation of Y.

[Joro Kolev]

Or if you were asking for the syntax of -sem-, just look at their diagrams and examples.

sem (Y <- x1 x2 etc) (x1 <- x2 x3 etc. )

[Artyom Mikhaylin]

Joro Kolev Yes, it's standard linear system. And i can build such systems.
Sorry, I forgot to clarify that in doing so I need to use 'ln' or 'sqrt' or multiplication, that is, the system will be nonlinear.
I specify the system

Y= c1 + b11 * ln(x1) + b12 * sqrt(x2) + b13 * x3 +b14* x3 *x4+ ...b1N * xN + e1
x1 = c2 + b22 * x2 + b23 * x3 + b2N * xN + e2

I apologize for not writing right away.

[Joro Kolev]

In econometrics, systems are (mostly) called linear when they are linear in the parameters.

So you just pre-generate your variables, e.g.,

gen sqX = sqrt(X)

gen lnX = log(X)

and then you use in your linear (in the parameters) system the generated variables.

[Artyom Mikhaylin]

Joro Kolev Thank you very much! Everything worked out. Similarly, I implemented multiplication, e.g.,

gen mp12=x1*x2

Do I understand correctly that it is impossible to realize the multiplication of this type as in regression: {x1}*x1*{x2}*x2 ?

Thank you for your help and patience!

[Myles Moore]

Could I get some clarification here?
If there is a non-linear transformation is required, such as x^2 or x^3, in the SEM model then would you not need to use the nlcom postestimation to get the one coefficient?

sem (y <- x x2)
nlcom _b[x]*_b[x2]

On a similar string, I am also curious how one would deal with a non-linear mediator (z) on our outcome (y), but this same mediator is linear with the other covariate (x)? I am guessing that there is an assumption here from my readingsthat I have missed.
e.g.

sem (y <- z z2) (x -> z z2) *there may be no direct link between y and x.
nlcom _b[z]*_b[z2]

[Anustup Kundu]

My question doesn't relate to SEM and nonlinear regression but towards nlcom I am trying to estimate the Intergenerational Correlation (IGC) in education using nlcom but cannot figure out how to

\[ IGC : \rho_{IG}= \beta1 * \frac{\sigma_{parent}}{\sigma_{child}} \]

Where P_IG = Intergenerational Correlation (IGC),

Beta1 = intergenerational regression coefficient (IGRC) coming from estimating

\[ Edu_{i,g} = \beta_{0}+ \beta_{1}Edu_{i,parent}+\beta_{2}Edu_{i,grandparen t} + \epsilon_{ig} \]

and Sigma= standard deviation of the parent/child