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Incorporating measurement error in n = 1 psychological autoregressive modeling.

Schuurman NK, Houtveen JH, Hamaker EL - Front Psychol (2015)

Bottom Line: Furthermore, we find that for realistic (i.e., small) sample sizes, psychological research would benefit from a Bayesian approach in fitting these models.Finally, we illustrate the effect of disregarding measurement error in an AR(1) model by means of an empirical application on mood data in women.We find that, depending on the person, approximately 30-50% of the total variance was due to measurement error, and that disregarding this measurement error results in a substantial underestimation of the autoregressive parameters.

View Article: PubMed Central - PubMed

Affiliation: Department of Methodology and Statistics, Utrecht University Utrecht, Netherlands.

ABSTRACT
Measurement error is omnipresent in psychological data. However, the vast majority of applications of autoregressive time series analyses in psychology do not take measurement error into account. Disregarding measurement error when it is present in the data results in a bias of the autoregressive parameters. We discuss two models that take measurement error into account: An autoregressive model with a white noise term (AR+WN), and an autoregressive moving average (ARMA) model. In a simulation study we compare the parameter recovery performance of these models, and compare this performance for both a Bayesian and frequentist approach. We find that overall, the AR+WN model performs better. Furthermore, we find that for realistic (i.e., small) sample sizes, psychological research would benefit from a Bayesian approach in fitting these models. Finally, we illustrate the effect of disregarding measurement error in an AR(1) model by means of an empirical application on mood data in women. We find that, depending on the person, approximately 30-50% of the total variance was due to measurement error, and that disregarding this measurement error results in a substantial underestimation of the autoregressive parameters.

No MeSH data available.


(A) Graphical representation of an AR(1) model. (B) Graphical representation of an AR(1)+WN model. (C) Graphical representation of an ARMA(1,1) model.
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Figure 1: (A) Graphical representation of an AR(1) model. (B) Graphical representation of an AR(1)+WN model. (C) Graphical representation of an ARMA(1,1) model.

Mentions: For a graphical representation of the model, see Figure 1A. A positive value for ϕ indicates that the score at the current occasion will be similar to that at the previous occasion— and the higher the positive value for ϕ, the more similar the scores will be. Therefore, a positive AR parameter reflects the inertia, or resistance to change, of a process (Suls et al., 1998). A positive AR parameter could be expected for many psychological processes, such as that of mood, attitudes, and (symptoms of) psychological disorders. A negative ϕ indicates that if an individual has a high score at one occasion, the score at the next occasion is likely to be low, and vice versa. A negative AR parameter may be expected for instance in processes that concern intake, such as drinking alcoholic beverages: If an individual drinks a lot at one occasion, that person may be more likely to cut back on alcohol the next occasion, and the following occasion drink a lot again, and so on Rovine and Walls (2006). An AR parameter close to zero indicates that a score on the previous occasion does not predict the score on the next occasion. Throughout this paper we consider stationary models, which implies that the mean and variance of y are stable over time, and ϕ lies in the range from −1 to 1 (Hamilton, 1994). The innovations ϵt reflect that component of each state score ỹt that is unpredictable from the previous observation. The innovations ϵt are assumed to be normally distributed with a mean of zero and variance .


Incorporating measurement error in n = 1 psychological autoregressive modeling.

Schuurman NK, Houtveen JH, Hamaker EL - Front Psychol (2015)

(A) Graphical representation of an AR(1) model. (B) Graphical representation of an AR(1)+WN model. (C) Graphical representation of an ARMA(1,1) model.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4516825&req=5

Figure 1: (A) Graphical representation of an AR(1) model. (B) Graphical representation of an AR(1)+WN model. (C) Graphical representation of an ARMA(1,1) model.
Mentions: For a graphical representation of the model, see Figure 1A. A positive value for ϕ indicates that the score at the current occasion will be similar to that at the previous occasion— and the higher the positive value for ϕ, the more similar the scores will be. Therefore, a positive AR parameter reflects the inertia, or resistance to change, of a process (Suls et al., 1998). A positive AR parameter could be expected for many psychological processes, such as that of mood, attitudes, and (symptoms of) psychological disorders. A negative ϕ indicates that if an individual has a high score at one occasion, the score at the next occasion is likely to be low, and vice versa. A negative AR parameter may be expected for instance in processes that concern intake, such as drinking alcoholic beverages: If an individual drinks a lot at one occasion, that person may be more likely to cut back on alcohol the next occasion, and the following occasion drink a lot again, and so on Rovine and Walls (2006). An AR parameter close to zero indicates that a score on the previous occasion does not predict the score on the next occasion. Throughout this paper we consider stationary models, which implies that the mean and variance of y are stable over time, and ϕ lies in the range from −1 to 1 (Hamilton, 1994). The innovations ϵt reflect that component of each state score ỹt that is unpredictable from the previous observation. The innovations ϵt are assumed to be normally distributed with a mean of zero and variance .

Bottom Line: Furthermore, we find that for realistic (i.e., small) sample sizes, psychological research would benefit from a Bayesian approach in fitting these models.Finally, we illustrate the effect of disregarding measurement error in an AR(1) model by means of an empirical application on mood data in women.We find that, depending on the person, approximately 30-50% of the total variance was due to measurement error, and that disregarding this measurement error results in a substantial underestimation of the autoregressive parameters.

View Article: PubMed Central - PubMed

Affiliation: Department of Methodology and Statistics, Utrecht University Utrecht, Netherlands.

ABSTRACT
Measurement error is omnipresent in psychological data. However, the vast majority of applications of autoregressive time series analyses in psychology do not take measurement error into account. Disregarding measurement error when it is present in the data results in a bias of the autoregressive parameters. We discuss two models that take measurement error into account: An autoregressive model with a white noise term (AR+WN), and an autoregressive moving average (ARMA) model. In a simulation study we compare the parameter recovery performance of these models, and compare this performance for both a Bayesian and frequentist approach. We find that overall, the AR+WN model performs better. Furthermore, we find that for realistic (i.e., small) sample sizes, psychological research would benefit from a Bayesian approach in fitting these models. Finally, we illustrate the effect of disregarding measurement error in an AR(1) model by means of an empirical application on mood data in women. We find that, depending on the person, approximately 30-50% of the total variance was due to measurement error, and that disregarding this measurement error results in a substantial underestimation of the autoregressive parameters.

No MeSH data available.