###[Note] I've decided to re-write my question for the sake of brevity. The original question can be found below.

Suppose a number of individuals fill in a questionnaire at a multiple number of time points. In other words, for each person $i \in \{1, \ldots, m\}$ and for each time point $t \in \{1,\ldots,T\}$, we have responses $\mathbf{y}_i^{(t)} = (y_{i1}^{(t)},\ldots,y_{ip}^{(t)})^{T}$ where $p$ is the number of items on the questionnaire.

I am interested in finding out which item responses cause/predict other item responses, preferably using network models. I need a model that can do this under the following conditions:

• all responses $y_{ik}$ are in some finite range (they're Likert responses)
• the data may not be stationary
• I would like to account for feedback loops. That is, at time 1 a response to item A might influence an response to item B at time 2, which might influence item A at time 3.
• An estimation of direction is required, i.e. I'm not only interested in correlation, but also direction.

###Original formulation of my question:

I'm trying to find a suitable model for a problem I've been asked to investigate.

Suppose a number of individuals fill in a questionnaire at a multiple number of time points. In other words, for each person $i \in \{1, \ldots, m\}$ and for each time point $t \in \{1,\ldots,T\}$, we have responses $\mathbf{y}_i^{(t)} = (y_{i1}^{(t)},\ldots,y_{ip}^{(t)})^{T}$ where $p$ is the number of items on the questionnaire.

I am interested in providing these persons with feedback regarding their responses, e.g. the course of outcomes to specific items, and relations between item-responses. In particular, I'm interested in estimating and visualizing a network model which is fitted to this data. The hope is that this network model can indicate which item-responses are predictive for other item-responses.

Granger-causality came to mind but it does not seem the best method here. For one, the data is categorical (Likert-scale) and not necessarily stationary. Also, normality usually cannot be assumed.

I am not interested in predicting anything, the most important feature is that one get's a sense of "what item-responses `predict' other item-responses?" What would be a proper model for this setting? Thanks in advance.

[Note] I've decided to re-write my question for the sake of brevity. The original question can be found below.

Suppose a number of individuals fill in a questionnaire at a multiple number of time points. In other words, for each person $i \in \{1, \ldots, m\}$ and for each time point $t \in \{1,\ldots,T\}$, we have responses $\mathbf{y}_i^{(t)} = (y_{i1}^{(t)},\ldots,y_{ip}^{(t)})^{T}$ where $p$ is the number of items on the questionnaire.

I am interested in finding out which item responses cause/predict other item responses, preferably using network models. I need a model that can do this under the following conditions:

• all responses $y_{ik}$ are in some finite range (they're Likert responses)
• the data may not be stationary
• I would like to account for feedback loops. That is, at time 1 a response to item A might influence an response to item B at time 2, which might influence item A at time 3.
• An estimation of direction is required, i.e. I'm not only interested in correlation, but also direction.

Original formulation of my question:

I'm trying to find a suitable model for a problem I've been asked to investigate.

Suppose a number of individuals fill in a questionnaire at a multiple number of time points. In other words, for each person $i \in \{1, \ldots, m\}$ and for each time point $t \in \{1,\ldots,T\}$, we have responses $\mathbf{y}_i^{(t)} = (y_{i1}^{(t)},\ldots,y_{ip}^{(t)})^{T}$ where $p$ is the number of items on the questionnaire.

I am interested in providing these persons with feedback regarding their responses, e.g. the course of outcomes to specific items, and relations between item-responses. In particular, I'm interested in estimating and visualizing a network model which is fitted to this data. The hope is that this network model can indicate which item-responses are predictive for other item-responses.

Granger-causality came to mind but it does not seem the best method here. For one, the data is categorical (Likert-scale) and not necessarily stationary. Also, normality usually cannot be assumed.

I am not interested in predicting anything, the most important feature is that one get's a sense of "what item-responses `predict' other item-responses?" What would be a proper model for this setting? Thanks in advance.

I'm trying to find a suitable model for a problem I've been asked to investigate.

Suppose a number of individuals fill in a questionnaire at a multiple number of time points. In other words, for each person $i \in \{1, \ldots, m\}$ and for each time point $t \in \{1,\ldots,T\}$, we have responses $\mathbf{y}_i^{(t)} = (y_{i1}^{(t)},\ldots,y_{ip}^{(t)})^{T}$ where $p$ is the number of items on the questionnaire.

I am interested in providing these persons with feedback regarding their responses, e.g. the course of outcomes to specific items, and relations between item-responses. In particular, I'm interested in estimating and visualizing a network model which is fitted to this data. The hope is that this network model can indicate which item-responses are predictive for other item-responses.

Granger-causality came to mind but it does not seem the best method here. For one, the data is categorical (Likert-scale) and not necessarily stationary. Also, normality usually cannot be assumed.

I am not interested in predicting anything, the most important feature is that one get's a sense of "what item-responses `predict' other item-responses?" What would be a proper model for this setting? Thanks in advance.

###[Note] I've decided to re-write my question for the sake of brevity. The original question can be found below.

Suppose a number of individuals fill in a questionnaire at a multiple number of time points. In other words, for each person $i \in \{1, \ldots, m\}$ and for each time point $t \in \{1,\ldots,T\}$, we have responses $\mathbf{y}_i^{(t)} = (y_{i1}^{(t)},\ldots,y_{ip}^{(t)})^{T}$ where $p$ is the number of items on the questionnaire.

I am interested in finding out which item responses cause/predict other item responses, preferably using network models. I need a model that can do this under the following conditions:

• all responses $y_{ik}$ are in some finite range (they're Likert responses)
• the data may not be stationary
• I would like to account for feedback loops. That is, at time 1 a response to item A might influence an response to item B at time 2, which might influence item A at time 3.
• An estimation of direction is required, i.e. I'm not only interested in correlation, but also direction.

###Original formulation of my question:

I'm trying to find a suitable model for a problem I've been asked to investigate.

Suppose a number of individuals fill in a questionnaire at a multiple number of time points. In other words, for each person $i \in \{1, \ldots, m\}$ and for each time point $t \in \{1,\ldots,T\}$, we have responses $\mathbf{y}_i^{(t)} = (y_{i1}^{(t)},\ldots,y_{ip}^{(t)})^{T}$ where $p$ is the number of items on the questionnaire.

I am interested in providing these persons with feedback regarding their responses, e.g. the course of outcomes to specific items, and relations between item-responses. In particular, I'm interested in estimating and visualizing a network model which is fitted to this data. The hope is that this network model can indicate which item-responses are predictive for other item-responses.

Granger-causality came to mind but it does not seem the best method here. For one, the data is categorical (Likert-scale) and not necessarily stationary. Also, normality usually cannot be assumed.

I am not interested in predicting anything, the most important feature is that one get's a sense of "what item-responses `predict' other item-responses?" What would be a proper model for this setting? Thanks in advance.