Some questions on simulations and why they are better than the computation of predicted values/probabilities
4 Aug
2011
4 Aug
'11
3:17 a.m.
Dear all,
I have a general question on the simulation technique developed in Zelig,
and available for estimating first differences and expected values of the
dependent variable for different quantities of interest of the independent
variables. It is not completely clear to me to what extent simulation
techniques are more suitable for this purpose than the simple computation of
predicted values (or probabilities). I understand the *logical* difference
between algebraic computation of effects, and the simulation of them. But
expected and predicted values are practically the same for the same model,
although derived with different methods. My question, then, is: is it only a
question of *methodological elegance* or are there strong theoretical
reasons for which we should prefer simulations over the computation of
predicted values/probabilities? And, are there statistical models for which
only simulations can be meaningfully used?
Thanks a lot in advance for your answers.
Mattia
--------------------------
(Mr.) Mattia Guidi
Ph.D Candidate
European University Institute
Department of Political and Social Sciences
Badia Fiesolana
Via dei Roccettini 9
I-50014 San Domenico di Fiesole (FI)
ITALY
4 Aug
4 Aug
10:20 a.m.
Hi, Mattia.
Simulation is computational easier for GLMs, survival models, etc. As you
increase the number of draws, you should get closer to the analytic
solution, in most cases. Zelig uses 1,000 simulations by default, which
should be enough to get you to 2 decimal places if your data are relatively
well-behaved. For some of the Bayesian models with unobserved DVs (e.g.,
irtkd), simulation is the only method of estimation.
In general, in Zelig-terminology, "expected values" refers to simulations of
the model parameters, which can be used to calculate the mean of the
distribution. For example, for a logistic model, both the model parameter
and the mean of the distribution would be pi (the probability of a 1,
conditional on X). We simulate n pi's to capture both the systematic and
stochastic variation in the model.
"Predicted values" in Zelig-terminology refers to draws from the statistical
distribution (which is on the same scale as the DV). To continue the logit
example, a simulated predicted value would either be a 0 or a 1. Taking the
mean of the predicted values output by Zelig should give you something close
to pi, the population parameter.
HTH,
Olivia
On Thu, Aug 4, 2011 at 3:17 AM, Mattia Guidi <mattiaguidi(a)gmail.com> wrote:
Dear all,
I have a general question on the simulation technique developed in Zelig,
and available for estimating first differences and expected values of the
dependent variable for different quantities of interest of the independent
variables. It is not completely clear to me to what extent simulation
techniques are more suitable for this purpose than the simple computation of
predicted values (or probabilities). I understand the *logical* difference
between algebraic computation of effects, and the simulation of them. But
expected and predicted values are practically the same for the same model,
although derived with different methods. My question, then, is: is it only a
question of *methodological elegance* or are there strong theoretical
reasons for which we should prefer simulations over the computation of
predicted values/probabilities? And, are there statistical models for which
only simulati ons can be meaningfully used?
Thanks a lot in advance for your answers.
Mattia
--------------------------
(Mr.) Mattia Guidi
Ph.D Candidate
European University Institute
Department of Political and Social Sciences
Badia Fiesolana
Via dei Roccettini 9
I-50014 San Domenico di Fiesole (FI)
ITALY
4672
days inactive
4672
days old
1 comments
2 participants
participants (2)
-
Mattia Guidi -
Olivia Lau