How do I calculate marginal effects of estimated parameters for binary data in lavaan?

[ykla...@gmail.com]

Dear Yves and lavaan users,

 

I am trying to interpret lavaan estimated parameters by calculating marginal effects. Can anyone tell me how I can calculate marginal effects? My understanding is that lavaan does not yet support logit and I cannot take the exponent of the estimated parameters.

 

Note: I am using imputed data and I am running lavaan through semTools.

 

Thanks,

John

[yrosseel]

On 11/30/2014 07:27 AM, ykla...@gmail.com wrote:
> Dear Yves and lavaan users,
> I am trying to interpret lavaan estimated parameters by calculating
> marginal effects.

What exactly do you mean with 'marginal effects'? Can you give an example?

Yves.

[ykla...@gmail.com]

Hi Yves,

 

I am trying to interpret the magnitude of the estimated parameter for a probit link (equivalent to odds ratio for logit link). How can I do that? I am using imputed data and semTools to run lavaan.

 

Thanks,

John

[yrosseel]

On 12/02/2014 05:09 AM, ykla...@gmail.com wrote:
> Hi Yves,
> I am trying to interpret the magnitude of the estimated parameter for a
> probit link

It is exactly the same as in probit regression. Think of the probits as
z-scores. Say you have a regression coefficient equal to 0.5. This means
that if you have a '1-unit-increase' (for x, which is perhaps the latent
variable), the probit value increases with 0.5.

In R, you can transform probits to probabilities by using pnorm().

Google around for 'probit coefficients', and you will find plenty.

Yves.

[Alban Ramette]

Dear Yves and lavaan users,

I have read that, in general, one cannot directly interpret the coefficients from the output of a probit regression. The way to go would be to interpret the marginal effects of the regressors, that is, how much the (conditional) probability of the outcome variable changes when you change the value of a regressor, holding all other regressors constant at some values. There are different choices to set those values apparently in the literature.
I am a bit confused now with your previous response. Could you clarify please?

I would like to apply lavaan to analyse binary outcome data and I have two additional questions:

1)      In logit and probit models, crude coefficients and adjusted coefficients for confounding effects can differ not only because of confounding but also because of a rescaling of the model. As such, logit or probit coefficients from different nested models are not measured on the same scale and are therefore not directly comparable.

Yet, it seems that it is what is done when one compares direct and indirect effects in sem interpretation. So my question is how much this statistical consideration invalidates the interpretation of direct vs. indirect relationships when some outcome variables are binary in a sem analysis.

2)      In the case of multivariable logit (or probit) regressions, Karlson and colleagues (2012 doi: 10.1177/0081175012444861  Sociological Methodology  August 2012 vol. 42 no. 1 286-313. Comparing Regression Coefficients Between Same-sample Nested Models Using Logit and Probit A New Method) develop a new method that gives unbiased comparisons of logit (or probit) coefficients of the same variable (x) across same-sample nested models successively including control variables (z).

Could such adjustments be made in lavaan?

(I noticed that the authors produced a STATA scripts and no R scripts).

many thanks in advance for your help.

Best regards,
Alban

[Yves Rosseel]

On 01/07/2015 06:03 PM, Alban Ramette wrote:
> Dear Yves and lavaan users,

> I have read that,in general, one cannot directly interpret the

> coefficients from the output of a probit regression. The way to go would
> be to interpret the marginal effects of the regressors, that is, how
> much the (conditional) probability of the outcome variable changes when
> you change the value of a regressor, holding all other regressors

> constant at some values.There are different choices to set those values

> apparently in the literature.
> I am a bit confused now with your previous response. Could you clarify
> please?

Well, you can do this yourself manually. Choose values for the
predictors (usually, for continuous predictors, we take the mean, for
categorical predictors, we take the most common category). Compute the
probit value (simply apply the regression formula), and transform to a
probability by using pnorm(). Next, you change the value of a single
predictor (say, from 10 to 11), while keeping all others predictors at
the same value. Compute the new probit value, and transform to a
probablity again.

> I would like to apply lavaan to analyse binary outcome data and I have
> two additional questions:
>

> 1)In logit and probit models, crude coefficients and adjusted

> coefficients for confounding effects can differ not only because of
> confounding but also because of a rescaling of the model. As such, logit
> or probit coefficients from different nested models are not measured on
> the same scale and are therefore not directly comparable.

So far, so good.

> Yet, it seems that it is what is done when one compares direct and
> indirect effects in sem interpretation.

But they are in the same model? I believe your concern, and the one
voiced by this paper:

Karlson and colleagues (2012 doi: 10.1177/0081175012444861Sociological
> Methodology August 2012 vol. 42 no. 1 286-313.

only applies if you fit different nested models. Or are you referring to
comparing 'c' versus 'c-prime'? Ie comparing the effect of X on Y in a
model without a mediator, versus the effect of X on Y in a model
including a mediator?

> Could such adjustments be made in lavaan?

Sure. You can use the := operator to define all the ingredients you need.

> (I noticed that the authors produced a STATA scripts and no R scripts).

I am afraid I have no time to do this myself. Perhaps some others on
this list want to volunteer?

Yves.

[Alban Ramette]

Thank you, Yves.
[ interpret the marginal effects of the regressors]

Well, you can do this yourself manually. Choose values for the
predictors (usually, for continuous predictors, we take the mean, for
categorical predictors, we take the most common category). Compute the
probit value (simply apply the regression formula), and transform to a
probability by using pnorm(). Next, you change the value of a single
predictor (say, from 10 to 11), while keeping all others predictors at
the same value. Compute the new probit value, and transform to a
probablity again.

Thanks for the clarification.
 

> I would like to apply lavaan to analyse binary outcome data and I have
> two additional questions:
>
> 1)In logit and probit models, crude coefficients and adjusted
> coefficients for confounding effects can differ not only because of
> confounding but also because of a rescaling of the model. As such, logit
> or probit coefficients from different nested models are not measured on
> the same scale and are therefore not directly comparable.

So far, so good.

> Yet, it seems that it is what is done when one compares direct and
> indirect effects in sem interpretation.

But they are in the same model? I believe your concern, and the one
voiced by this paper:

Karlson and colleagues (2012 doi: 10.1177/0081175012444861Sociological Methodology  August 2012 vol. 42 no. 1 286-313.

only applies if you fit different nested models. Or are you referring to
comparing 'c' versus 'c-prime'? Ie comparing the effect of X on Y in a
model without a mediator, versus the effect of X on Y in a model
including a mediator?

My initial impression was that in the sem approach when one compares the direct effects of (X on Y) vs. the indirect effects (X on Y including a mediator, or any other Z variable), we would be in the same situation as described in the abovementioned paper. Hence the need to disentangle the part of the variation coming from rescaling from that coming from confounding.
OK. So it seems that the sem approach is not affected by this consideration because indeed we are not dealing with nested models in the sem approach.

Thanks for your help.