Dear all,
I am responding to reviewers' comments on a paper in which we modeled instantaneous driving decisions (decisions taken by drivers in longitudinal direction such as acceleration/deceleration) based on real world data. In order to help the experts over here understand my query, I will briefly explain the context of the study. My apologies for the long post or if it is irrelevant to the scope of Statalist.
In the study, we assumed presence of two distinct yet unobserved regimes and the research issue is to characterize and quantify these regimes in typical driving cycles, explore when the two regimes change and the key correlates associated with each typical driving profile regime. We also considered higher dimension (> than 2 regimes) models but i will keep this query to only two-regimes for simplicity.
Within this premise, we used Markov switching models which Stata also provides in its mswitch command (http://www.stata.com/manuals14/tsmswitch.pdf). Given the high frequency of our data i.e. second-by-second data on instantaneous driving decisions, I used Markov-Switching models where the transition of driving profile between two regimes is abrupt, which Stata calls Markov Switching Dynamic Regression (MSDR) framework (mswitch dr). In the literature, high-frequency data is usually modeled with MSDR as opposed to modeling low-frequency data with Markov Switching Auto-regressive Regression (MSAR) where auto-regressive terms of nth order can be included in the modeling specification.
Markov-switching regression models specify that the unobserved regime indicator "St" follows a first-order Markov chain where the probability that "St" is equal to j ∈ (1, 2) depends only on the current state/regime and not previous history. Though the assumption of first-order Markov chain in this setting is fairly common in the literature, a reviewer asked us if this assumption may be restrictive as future driving decisions can not only depend on current state, but also previous history due to "delay in human perception and vehicle actuators." Alternatively, based on what i understand, this implies that current regime can depend on lagged values of dependent variables (Auto-regressive components) and/or error terms (Moving average)? These features are provided by mswitch ar where user can define auto-regressive components through the ar(n) option. To me, this seems like i can also use mswitch dr (instead of using mswitch ar) by manually including lags of dependent variable using Stata's time-series operators. The results of using mswitch ar with ar(n) and mswitch dr with lags defined by time-series operator are approximately similar.
My questions are:
Sincerely,
-Behram
I am responding to reviewers' comments on a paper in which we modeled instantaneous driving decisions (decisions taken by drivers in longitudinal direction such as acceleration/deceleration) based on real world data. In order to help the experts over here understand my query, I will briefly explain the context of the study. My apologies for the long post or if it is irrelevant to the scope of Statalist.
In the study, we assumed presence of two distinct yet unobserved regimes and the research issue is to characterize and quantify these regimes in typical driving cycles, explore when the two regimes change and the key correlates associated with each typical driving profile regime. We also considered higher dimension (> than 2 regimes) models but i will keep this query to only two-regimes for simplicity.
Within this premise, we used Markov switching models which Stata also provides in its mswitch command (http://www.stata.com/manuals14/tsmswitch.pdf). Given the high frequency of our data i.e. second-by-second data on instantaneous driving decisions, I used Markov-Switching models where the transition of driving profile between two regimes is abrupt, which Stata calls Markov Switching Dynamic Regression (MSDR) framework (mswitch dr). In the literature, high-frequency data is usually modeled with MSDR as opposed to modeling low-frequency data with Markov Switching Auto-regressive Regression (MSAR) where auto-regressive terms of nth order can be included in the modeling specification.
Markov-switching regression models specify that the unobserved regime indicator "St" follows a first-order Markov chain where the probability that "St" is equal to j ∈ (1, 2) depends only on the current state/regime and not previous history. Though the assumption of first-order Markov chain in this setting is fairly common in the literature, a reviewer asked us if this assumption may be restrictive as future driving decisions can not only depend on current state, but also previous history due to "delay in human perception and vehicle actuators." Alternatively, based on what i understand, this implies that current regime can depend on lagged values of dependent variables (Auto-regressive components) and/or error terms (Moving average)? These features are provided by mswitch ar where user can define auto-regressive components through the ar(n) option. To me, this seems like i can also use mswitch dr (instead of using mswitch ar) by manually including lags of dependent variable using Stata's time-series operators. The results of using mswitch ar with ar(n) and mswitch dr with lags defined by time-series operator are approximately similar.
My questions are:
- Does including lag(s) of dependent variables as independent variable help in relaxing the restriction put by first-order markov chain in mswitch? If not, how Stata deals with relaxing this assumption?
- When I do so, the lags of dependent variables are statistically significant (as it should be) but it absorbs the statistical significance of other covariates in the two regimes (which is also common). However, our focus is to study the correlations between regime-dependent response variable and key explanatory variables and not to develop a solid forecasting model per se. Can this help me in justifying not using lags? Also, note that the models with lagged dependent variables have poor goodness-of-fit (higher AIC, BIC, CAIC scores) compared to the ones without lagged dependent variables on right hand side.
- Do I really need to worry about the implications of first-order Markov Chain assumption? This assumption has been widely used in almost all the studies using this modeling framework. Based on my literature search, it seems that MSAR (i.e. mswitch ar) are not often used for high frequency data (second by second) similar to our data.
Sincerely,
-Behram
