 Resolving endogeneity using mixture m...    Message/Author  Michel van der Borgh posted on Tuesday, September 17, 2013 - 5:20 am
Hi,

I want to estimate a model but have a potential bias due to endogeneity. The problem is that I do not have reliable Instrumental Variables. I know that researchers have developed �frugal� IV methods to address this problem. These methods resolve the endogeneity problem without using observable instruments (e.g., Ebbes et al. 2005). The key idea of this approach is to introduce a binary unobserved IV that partitions endogenous predictors into two components, one uncorrelated and the other correlated with the error term in the main equation.

A simple model would look like:
Y(i) = b0 + b1*m1 + e(i),
M(i) = t*z(i) + v(i),

With i = 1, �., n and t an (m x 1)-vector of category means. z(i) is an unobserved discrete instrument (> 1 categories). It is assumed that z is independent of the error terms (e, v).

My question is how to implement this (if possible) in Mplus?

Ebbes, Peter, Michel Wedel, Ulf B�ckenholt, and Ton Steerneman (2005), �Solving and Testing for Regressor-Error (in)Dependence When No Instrumental Variables Are Available: With New Evidence for the Effect of Education on Income,� Quantitative Marketing and Economics, 3 (4), 365�92.

Best,
Michel  Bengt O. Muthen posted on Tuesday, September 17, 2013 - 1:14 pm
Just to clarify, what is M(i) and what is m1?  Michel van der Borgh posted on Tuesday, September 17, 2013 - 2:36 pm
Dear Bengt,

sorry for the confusion.

They are the same and indicate the beta-coefficient. The m stands for mediator in the original model. Both terms should be x(i).

Hope this clarifies things.

Best,
Michel  Bengt O. Muthen posted on Friday, September 20, 2013 - 5:47 pm
I think you are writing out eqn (1) in the Ebbes et al article. Eqn (1) says that z_i is a latent variable and pi is observed, which makes x_i a latent variable. So in Mplus you would say:

Model:

x BY;
z BY x@pi;
y ON x;

Perhaps there are several z variables, I don't know. If this model is identified, Mplus can estimate it.  Lucy Busija posted on Thursday, November 28, 2013 - 9:37 pm
Hello,
I am trying to estimate a model that is similar to Michael's above, with random effects for the instrumental variable.

I have a dichotomous outcome (0,1) and a continuous predictor and I am trying to find a break point in the predictor that best separates 0s from 1s on the outcome variable.

the model is specified as follows:
x BY;
x@1;
z BY x@predictor;
outcome ON x;

My questions are:
is this correct specification to address my question?
is the threshold value for outcome\$1 in the output my break point?
how do i introduce random effects of time of day onto z into the equation?

Thankyou in anticipation  Bengt O. Muthen posted on Friday, November 29, 2013 - 9:25 am
I don't understand this model - how a break point is explored.  Lucy Busija posted on Friday, November 29, 2013 - 1:02 pm
I would like to apply the instrumental latent variable approach (Ebbes 2005) to find a 'threshold' point on a continuous predictor, above which outcome of 1 is more probable than outcome of 0. The threshold is unknown in advance and needs to be estimated. Essentially, 'threshold' behaves like an instrumental variable (z_i in Ebbes 2005 eqtn (1)) in a sense that it 'decomposes x into a systematic part that is uncorrelated with error term and one that is possibly correlated with error term'.

Is there a way to estimate this type of model in Mplus?

Also, the dataset that I work with contains repeated observations for each person and I would like to use this information to derive random effects of a person on the 'threshold'. Again, is there a way to do this in Mplus? (the data are in a long format.)  Bengt O. Muthen posted on Friday, November 29, 2013 - 5:23 pm
I am not familiar with that approach so I can't say if it can be done in Mplus. There is not an automatic IV estimator in Mplus.

Random effects can be handled in Mplus in both single-level and two-level models.  Lucy Busija posted on Friday, November 29, 2013 - 11:57 pm
Thank you for clarifying, Dr Muthen. There is an alternative model that I would like to explore: dose-response threshold (Hunt, DL, Rai, SN. A new threshold dose-response model including random effects for data from developmental toxicity studies. J Appl Toxicol. 2005;25:435�439).
The model summarises the relationship between a continuous predictor and an outcome (0,1). It assumes the existence of a threshold: no association between outcome and predictor below the threshold and a logistic association above the threshold. Mathematically, the model takes on the following form:
Logit(P_ij) = {beta_0 + sigma_ij, for d_i< tau
Logit(P_ij)= {beta_0 + beta_1(d_i - tau) + sigma_ij, for d_i >= tau

where P_ij is the probability of outcome at jth time for ith individual (i = 1, . . . g; j = 1, . . . , m_i);
tau is the threshold level of the predictor (unknown in advance);
d_i is the observed level of the predictor;
beta_0 is the 'background' response;
beta_1 is the slope above threshold;
sigma_ij is the random effect.
According to Hunt and Rain (2005), the �model corresponds to the random effects logistic model � when tau = 0".

So my question is: can this type of model be programmed to run in Mplus and if so, would it be possible to model tau as a random parameter?  Lucy Busija posted on Sunday, December 01, 2013 - 6:16 pm
Further to my post above (and to simplify my question):
in essence, i have three sets of equations to estimate simultaneously.

1: Outcome=beta0_1+beta1_1(log_predictor)+beta2_1(log_predictor**2);

2: tau=exp(1�beta1_1/(2*beta2_1));

3: Outcome=beta0_2+beta1_2(predictor-tau);

is this possible to implement in Mplus in a single step?  Y.A. posted on Wednesday, May 09, 2018 - 9:18 pm
Dear Prof. Muthen,

I am having the similar trouble with the instrumental variables. The reviewer of my manuscript asked me to add instrumental variables which I am not able to find. The difference between my situation and the ones mentioned by colleagues above is that, my predictor and outcome are latent classes. I have one 3-class predictor and one 3-class outcome (this is the class solution I have now, without the instrumental variables).

Could you help me out here how to incoporate the latent classes into the eq (1) in Ebbes et al. 2005 please?

yi = b0 + b1x1 + ei
xi = pi'zi + vi

Besides, why the code example you gave on September 20, 2013 - 5:47 pm has no indicator?

x by;

Thank you very much!

Best regards,

YA  Bengt O. Muthen posted on Thursday, May 10, 2018 - 3:20 pm
I am not familiar with Ebbes approach - try SEMNET instead.

x BY; is a trick to get a latent variable X that is then used for some purpose.    Topics | Tree View | Search | Help/Instructions | Program Credits Administration