Dear colleagues, there are many commands in R that makes available to the researcher to make simulations using some Rasch models. However, I do not know any command or syntax in R that is suitable to the researcher he/she performs simulations of an individual, using dynamic Rasch models. I would be very grateful if anyone can show me any command or syntax suitable for simulations of a single person using dynamic Rasch models.
Best regards,
Cristiano.
An interesting paper proposes an R algorithm to estimate students' learning using dynamic Rasch, however the algorithm depends on using groups of students to estimate the parameters.
Article Dynamic estimation in the extended marginal Rasch model with...
Dear Cristiano,
I am not familiar with dynamic Rasch models, but in univariate time series, we can have, in the simplest scenario, AR, MA, ARMA, or ARIMA models. Each make different assumptions about how the value in the present affects the value of the same variable in the future. Using any of these models to, first, calculate the dependencies of theta in time, then you can set the item parameters as fixed for all time points, and then apply the Rasch model for simulating the responses for each time points.
In terms of estimating the parameters of this model, I believe a dynamic Rasch model can be derived from Hidden Markov Models and then any ML or Bayesian method can be applied. Hit me up if I can give any specific help regarding the cited procedures/methods.
Best!
thanks Víthor.
Your suggestion is interesting and, I believe, was applied in some packages.
eRm does that, for example, when applying AR model to insert the parameter of learning.
However, all of them seems to demand that the thetas and items parameters are estimated based on certain group of persons. I do not know whether the rationale of IRT permits that the thetas and items can be estimate based on an individual.
Besides, the use of AR, MA ARMA and ARIMA seems to be not very suitable in my interests, since they demand that the data are stationary, which is not the case in psychological tests based on performance, such as intelligence tests. ARIMA, for example, deals with the trend through the parameter I transforming the time series in a stationary series. This transformed series is used to predict the next time points.
If you have more ideas about this issue, I will be very glad to learn with you .
best wishes my friend
Hi Cristiano,
Please, clarify something for me: your issue is about data simulation of a binary dynamic process or is it about model estimation?
I also believe it is important to note that ARIMA can deal with first moment non-stationarity, as you said, with the I parameter. However, because with are talking about latent variable modeling, I am not quite sure how to proceed with tuning of this parameter in this case. Anyhow, with a fixed parameter I, I believe that a type of HMM-ARIMA or Rasch-ARIMA model can be used for both estimation and data simulation.
I would proceed with something like: first, I believe it is reasonable to assume that the b_i parameter of the Rasch model is fixed over time; the item's difficulty should be somewhat the same over a case study with a single individual. From this assumption, changes in the probability of responses (in a Rasch model) are due exclusively to changes in theta. Theta, then, can be modeled by an ARIMAX or a STL like model. ARIMAX is the same as ARIMA, but with an eXogenous variable (which can be set to be the time point, t, so trends are directly estimated, for instance, like random effects on the latent intercept of theta). STL is a procedure for time series decomposition which assumes that the time series Y can be decomposed by a seasonal component, a trend component, and a noise component. Because we are talking about latent variable modeling, I think it is reasonable to assume local independence of responses in the same t, but responses in previous t can influence responses in the current t. It is also reasonable to set a linear model for changes in theta. This is due to the fact that the Rasch model assumes the latent variable to be measured in an interval level; therefore, we can only estimate additive changes. Therefore, the responses could be estimated with something like (where I(·) is an indicator function and t = 0, 1, 2, 3, ..., n): X_jt = I{theta_t - b_j}; theta_t = beta0_j + beta1*theta_{t-1} + beta2*epsilon_{t-1} + epsilon_t; and beta0_t = w0 + w1*t
This is of course just a modeling exercise based on some general modeling principles. But maybe we can do a simulation to see if the model works as expected :)
Interesting. If the thetas can be estimated only based on the performance from only an individual, it's great.
May I invite you to discuss these ideas with a colleague, Enio Jelihovschi, which is working with me in this question? Enio is a good friend. I believe you will enjoy him. He has a PhD in Statistics from University of California, Berkeley.
Hope you like the idea
My best,
Yes, let us discuss these ideas with Enio.
I will send you a private message :)
Best,
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