Emotion regulation dynamics predict substance use in high-risk adolescents

Abstract

Emotional factors such as stress and anxiety contribute to risk of substance use in adolescents. Descriptive measures of within-person affect variability are often used to predict morbidity, but indices derived from theoretical models may provide more interpretable alternatives. A continuous-time state-space model of emotion regulation as closed-loop feedback control was used to estimate the homeostatic tendency of affect in each of 94 adolescent participants. The resulting indices of emotion regulation were then compared to within-person affect sum score means and standard deviations in predicting total counts of nicotine, alcohol, and cannabis use. Model-based emotion regulation was significantly associated with lower frequencies of nicotine, alcohol, and cannabis use, while mean negative affect sum score was associated with higher frequencies. Model comparisons revealed that while model-based predictors and descriptive statistics explained similar amounts of variance in substance use, the explained variance proportions were independent between the approaches. The greatest predictive value was achieved by a combined model with both sets of affect indices. We conclude that theoretically defined and model-estimated individual characteristics may serve an important role in conceptualizing and predicting substance use behavior.

1. Introduction

Motivation to use psychoactive substances can arise both as a cause and a consequence of problems with emotion regulation. Data collected from psychological and behavioral time series designs, known as Ecological Momentary Assessment (EMA, Shiffman, Stone, & Hufford, 2008) or Experience Sampling (Hektner, 2007), present new opportunities to conceptualize emotion regulation in terms of variability in emotional states over time. Often, individual traits of emotion regulation are inferred from descriptive statistics, such as the means and standard deviations of repeated, within-person assessments of affect. Descriptive indices are simple to compute and can be used as general predictors, but they are difficult to interpret in terms of real-world concepts, saying little about the actual process of change in emotion over time. An alternative approach is to specify theoretical models that describe the structure of emotion variability in terms of its mechanisms. Indices with unambiguous, a priori interpretations can then be obtained as the statistical parameter estimates from such models. In the current study, we compared one such theoretical index of emotion variability to commonly used descriptive statistics for their capacity to predict substance use.

In psychiatric research, self-reported affect assessments have been used in many ways. As a general state-based assessment of subjective experiences, they can provide insight into the timing and valence of emotions linked to psychiatric symptoms and episodic behaviors. For instance, positive and negative affect have been studied to differentiate between mood disorders (Brown, Chorpita, & Barlow, 1998) and as a means to identify distinctive features of anxiety and depression for the DSM-5 (Watson, Clark, & Carey, 1988; Watson, 2005). Negative affect has been associated with both binge eating severity and comorbidity with depression (Stice et al., 2001). A review of studies on smoking, stress and negative affect points to a general mediating or moderating role of negative affect in smoking initiation, maintenance, and relapse (Kassel, Stroud, & Paronis, 2003). Smoking to cope with negative affect is associated with higher risk for regular, persistent use, and with greater difficulty quitting than occasional social smoking (Debevec & Diamond, 2012; Brandon, 1994).

With time-series of affect data, (i.e., frequently repeated measures), patterns of change can help to identify new, distinguishing features of psychiatric disorders. For instance, the mean and overall variability of negative affect are greater in patients with borderline personality disorder than healthy controls (Ebner-Priemer et al., 2015). Intraindividual variability has been found to uniquely predict aspects of personality when compared to simple means (Eid & Diener, 1999; Kuppens, Mechelen, Nezlek, Dossche, & Timmermans, 2007). In clinical samples, the variability of momentary affect has been important to predicting and preventing behaviors and negative health outcomes, such as stress-induced binge eating (Agras & Telch, 1998; Stice, Akutagawa, Gaggar, & Agras, 2000; Stice, Presnell, & Spangler, 2002), relapse to alcohol, (Cooney, Litt, Morse, Bauer, & Gaupp, 1997; Witkiewitz & Marlatt, 2004; Gottfredson & Hussong, 2013) tobacco (Shiffman & Waters, 2004; O’Connell & Shiffman, 1988) and other substance use, prodrome to manic and depressive episodes (Wichers et al., 2010; Peeters, Berkhof, Delespaul, Rottenberg, & Nicolson, 2006), and suicide (Palmier-Claus, Taylor, Gooding, Dunn, & Lewis, 2012).

In this study, we conceptualize emotional variability in terms of feedback control and derive a measure of emotion regulation based on simple theoretical assumptions. Specifically, we assume that emotional states trend toward a mean or equilibrium value following stressful or joyful experiences. For short-term emotional stability, the rate at which emotions decay toward equilibrium, or their “offset”, must be sufficient to overcome perturbations, or their “onset”, from typical daily experiences (Hollenstein, Mcneely, Eastabrook, Mackey, & Flynn, 2012). Maintaining emotional homeostasis allows one to more easily predict and control one’s own behavior. Recovery from stress involves deactivation of flight or fight response and restfulness associated with the parasympathetic nervous system (Koole, 2009; Appelhans & Luecken, 2006; Hollenstein et al., 2012) and a renewal of the capacity for healthy behaviors. Positive experiences, while desirable, nonetheless can lead to poor judgment if their effects accumulate unchecked, a scenario characterized by mania (Gruber, Johnson, Oveis, & Keltner, 2008). Mechanisms of emotion regulation likely vary individually by development and preference. Family and friends may serve as sources of regulatory feedback, providing social support and stable interpersonal roles (Zaki & Williams, 2013; Marroquin, 2011). Intrinsic mechanisms of emotion regulation can include habits and tools of self-care, such as exercise, diet, structure and schedule, and cognitive-perceptual appraisal of experiences (Gross, 1998), all of which modulate the degree to which experiences disturb one from an equilibrium state and the time needed to recover.

The above concepts of emotional homeostasis, including equilibrium, disturbance, and rate of recovery, comprise the fundamental components of a feedback control system. The simplest case of linear feedback control subject to random perturbations can be formalized as a stochastic differential equation (SDE):

$$\frac{d{x}_t}{dt}=\lambda x_t+w_t,w\sim N\left(0,{\sigma }_w\right),$$ (1)

where x_t is the state of affect at time t, λ is the coefficient of feedback, and w_t is a random, exogenous disturbance at each time. If λ has a negative value, then on average, deviations from equilibrium are counteracted proportional to their magnitude. Variability at time t is driven by random disturbances, w_t, leading to a continual flux between perturbations and regulation. Similar models have previously been used to characterize affect change and have been fit to empirical data (Oravecz, Tuerlinckx, & Vandekerckhove, 2011; Deboeck & Bergeman, 2013).

The regulation parameter in Eq. 1, λ, is difficult to interpret in real-world terms. For a more intuitive index of emotion regulation, δ, we can define regulation as the percent recovery to equilibrium after a given time interval. This can be computed from λ in Eq. 1 by considering an equivalent, discrete-time formulation as an autoregressive model:

$$x_t=\beta x_{t-\mathrm{\Delta }}+\sqrt{\mathrm{\Delta }}{w}_t$$ (2)

$$\beta ={\mathbf{e}}^{\lambda \mathrm{\Delta }}$$ (3)

In this form, values of β from 0 to less than 1 characterize negative feedback or stabilization. In the current study, affect was assessed multiple times per day to study hourly variability. If we choose Δ =1 h, then β is the percentage of deviation from equilibrium remaining from the previous hour. We can therefore take the effect size of emotion regulation as 1 – β, interpreted as the expected percentage of recovery to equilibrium per hour given no further disturbances to affect.

In addition to the feedback coefficient λ, σ_w is the estimable standard deviation of exogenous disturbances. When the latent state describes affect or other subjective measures in the EMA context, such exogenous disturbances represent the distribution of unmeasured influences on the individual.

Together, the parameters λ and σ_w can be estimated from each individual’s time series to obtain indices of emotion regulation and volatility or sensitivity, respectively. One potential benefit of theoretical indices such as these is that their underlying theory can be validated and improved through empirical applications. If the feedback control structure is an accurate representation of emotional processes, then associations between its indices and substance use can be expected to arise for several reasons, depending on the particular effects of each substance. Drugs such as nicotine (Brandon, 1994; Carmody, 1992) and alcohol (Gottfredson & Hussong, 2013) may directly decrease average emotional volatility by dulling emotional responses. Whether these drugs are used to reduce emotional sensitivity or increase emotion regulation response depends on their timing as preemptive or reactive to stress, respectively. Conversely, many stimulants are used specifically for their ability of induce or sustain mania-like symptoms, potentially undermining the goals of healthy regulation.

We hypothesized that our theoretical, model-based indices of emotion regulation would predict substance use independently from simpler descriptive statistics. We did not hypothesize about the degree to which descriptive statistics would associate with substance use, but included them in analyses as a benchmark for methodological improvement.

2. Methods

The available EMA data presented many technical, methodological challenges, and required multiple steps of processing. In this section, we detail the sample, our quality control criteria, a state-space affect model, and the second stage regression of substance use onto the estimated parameters from that model. Our analysis was organized as follows: (1) In each individual, data quality was first determined in terms of complete rows of data and the information content of responses; (2) If the quality control criteria were met, then affect indicators were aggregated into negative affect scores; (3) Descriptive statistics and state-space model parameters were estimated from the aggregate scores, and counts of reported use for each substance were summed; (4) After steps 1–3 were performed for all individuals, counts of usage for each substance were regressed on the descriptive statistics and state-space model parameters. Each of these steps is detailed in the sections that follow.

Participants

This study utilizes data from the Social-Spatial Adolescent Study, a two-year longitudinal investigation of the interacting effects of peer networks, urban environment, and substance use (Mason et al., 2017). Participants were recruited between November 2012 and February 2014. Most participants (72%) were recruited from an urban adolescent medicine primary care clinic at Virginia Commonwealth University Medical Center, in Richmond, Virginia. Age-eligible (age 13 or 14) adolescents presenting to the clinic for routine or acute care were approached and invited to participate in this study by a research assistant. Other participants were recruited from a city health district satellite clinic, located within a subsidized housing development. These participants were recruited by referral to the study team from the primary Patient Advocate at the satellite clinic. Enrollment and data collection procedures were the same across sites. Chi-square tests revealed no significant differences in age, sex, or race of participants between the two recruitment sites. Race was not used because the sample was 86% African American and too small to estimate or control for any effects of demographic heterogeneity.

Ecological Momentary Assessment Moods

All participants were given a smart phone for the period of the study, through which EMA surveys were delivered. EMA surveys were administered to each subject via text message with an embedded URL link 18 times over a four-day period every other month, over a period of two years. The 11-item survey asked participants to rate their current mood in terms of happiness, sadness, anger, worry, loneliness, and stress as well as feelings of safety, on a scale of 1 to 9 with 9 representing more intense feelings. Participants were asked questions about if they were using tobacco, alcohol, and marijuana with responses coded as yes = 1, and no = 0. Participants were encouraged to complete each of the surveys within an 8-min window from when it was sent. Timestamps on each EMA survey were collected to identify surveys that were answered within the prescribed time limit.

Dimension reduction

It is common to aggregate information across affect items to simplify models and produce a small set of variables with maximal information content. For state-space models, it is necessary to aggregate discrete, Likert-type variables to produce a sufficiently continuous sample space to be described by the differential equation model. If all response categories are used, then uniquely weighted combinations of the 7, 11-point affect items would produce an affect dimension with up to 11⁷ possible values. In practice, most participants only use a small subset of the available response categories, making dimension reduction necessary.

Table 1 shows that all affect items were moderate to highly correlated across individuals and waves. Items ”happy” and ”safe” were positively correlated with each other and negatively correlated with all other items. The strong inter-correlations suggest that the indicators may be related to one or two underlying dimensions.

Table 1.

Correlation matrix of affect states across the total sample.

	Happy	Angry	Safe	Lonely	Anxious	Sad
Angry	−0.47
Safe	0.35	−0.3
Lonely	−0.35	0.55	−0.29
Anxious	−0.34	0.58	−0.33	0.57
Sad	−0.43	0.67	−0.32	0.61	0.63
Stressed	−0.42	0.64	−0.32	0.59	0.66	0.68

When affect questionnaire items must be aggregated into a single dimension of affect, a common strategy is to sum the scores across all items for each measurement occasion. To produce a methodological standard for comparison, we computed series of sum scores for each person along with their person-level means and standard deviations. Items “happy” and “safe” were first negatively coded, then all items were added together to produce a series of negative affect sum scores for each person.

To produce negative affect series for the state-space model, an alternative dimension reduction technique was used. Sum scores imply two untenable assumptions. First, that all items are equally important to the underlying dimension, and second, that no item-level variance is due to measurement error or other sources irrelevant to their collective underlying dimension. A standard alternative approach to aggregation is to produce scores from a factor model, or as an approximation, principal component analysis. These options weight the items by their communality, or the inter-correlation of each with the other items. Scores representing the shared variance of the items are produced that exclude item-specific, residual variance. One rapid method of computing principal component scores is Singular Value Decomposition (SVD). SVD is given for m × n data matrix X as X = UΣV^T, where U contains n length-m orthonormal columns of scores, V is the n × n matrix of eigenvectors, and Σ is the n × n diagonal matrix of eigenvalues. The first column of U provides a set of weighted composite scores that maximally account for the shared variance of the items. Subsequent columns account for diminishing proportions of the total variance of the items, and variance unique to particular items is relegated to the last columns in the U matrix. Items ”safe” and ”happy” were automatically reverse coded by the SVD as a result of their negative correlations with the other items. Only a single variable maximally representing negative affect was of interest in this application, so only the first column of the U matrix was used to represent affect principal component scores, and the others were discarded. Affect items were standardized and SVD was applied separately for each wave and for each person, allowing the respective influence of each affect indicator to vary individually. This choice is analogous to relaxing the assumption of factor loading invariance in a factor analysis. The exact loading structure and its reliability were of less concern than the aggregation of available information across the items within each person’s time series.

Model

The measurement intervals of each series were unequal, so a continuous-time state-space model (SSM) as shown in Eq. 1 was used to model the reduced series of negative affect data as an SDE:

$${\dot{x}}_t=\lambda \left(x_t-{\mu }_x\right)+w_t,w_t\sim N\left(0,{\sigma }_w\right).$$ (4)

$$y_t={\mu }_y+x_t+{\in }_t,{\in }_t\sim N\left(0,{\sigma }_{\in }\right).$$ (5)

The additional, second Eq. (5) relates observed measures y_t to the latent state by a constant mean μ_y and measurement error ∈_t. Because affect indicator scores were standardized, the mean or equilibrium value of the state equation, μ_x was fixed to zero and the indicator means, μ_y, were subtracted out. Individual emotional resilience was calculated as δ =1 e^λ, as described by Eqs. (2) and (3). Because as many as 18 repeated measures were taken over the course of each four day burst, we coded the time intervals to a scale of hours such that Δ =1 h. δ is therefore interpreted as the expected percentage of emotional recovery to baseline over the course of 1 h absent the effects of additional disturbances.

The SDE model was implemented using the Kalman filter (Kalman & Bucy, 1961), an optimal method of obtaining minimum-variance, unbiased estimates of latent states from noisy indicators and fitting time series models to data. Waves of negative affect SVD scores were aggregated in a multi-group manner within the state space model with the first observation of each wave beginning at hour 0. Maximum likelihood and the Nelder-Mead optimization algorithm (Nelder & Mead, 1965) were used to estimate the parameters in R (R Core Team, 2018). Waves were far enough apart in time to be modeled independently with each starting over at time zero. Each parameter was estimated between-waves for sufficient statistical power. The first observation of each wave was used as the initial position of the latent state and the series variance as the initial state variance.

Cross-sectional Analysis

The indices of emotion regulation, δ and σw, were estimated for each individual along with the means (μ_SS) and standard deviations (σ_SS) of negative affect sum scores. These within-person statistics were then used as the independent variables in a between-person analysis of aggregate counts of substance use. Total counts of nicotine, alcohol, and cannabis use were produced from the EMA data. Counts of each substance were overdispersed for a Poisson model, so they were regressed upon the extracted affect variables using multiple negative binomial regression. To estimate the uniqueness and contribution of the model-based predictors to the total explained variance of substance use, substance use counts were regressed onto: (a) only the mean and standard deviation of affect sum scores; (b) only the model-based predictors, emotion regulation and volatility; (c) predictors from both (a) and (b) combined. The magnitude and uniqueness of improvement in R² due to the model-based predictors was then quantified from comparisons of the three models. Nagelkerke’s generalized R² (Nagelkerke, 1991) was used for the negative binomial regressions with the recommended adjustment for discrete likelihood functions.

Preprocessing and quality control

Data were preprocessed to ensure that only time series with the necessary quality requirements were used in the analysis. Statistics drawn from inadequate samples will be highly variable and add noise to any subsequent relationships with covariates. In two-step analyses such as this, uninformative or misleading response patterns may reduce statistical power of the final analysis by reducing the estimable effect sizes, regardless of the number of people in the total sample. Data quality metrics included a minimum number of complete rows of data (6 per wave, 18 total per person) and a minimum amount of available affect information per wave. Many participants did not provide enough usable information, either using most affect items in a sparse, binary way, or entering only a single rating for all occasions. Data were frequently missing, so the amount of remaining data per wave was small and thus sensitive to bias introduced by interpolation. To avoid this risk, rows with missing data were simply excluded.

Variables with zero variance lead to singular matrices in computation of the model expectations and likelihood values. For integer-valued variables such as ordinal Likert scales, low variance is associated with only rarely using more than one response category. Such cases can produce erratic results and model-fitting errors in state-space models, which assume continuous variation in the sample space. If too few items were used in a nuanced way, for instance with no variability on some and binary responses on others, then the resulting SVD scores or other representations of the latent dimensions will be too coarse to model reliably. To address uninformative response patterns, Shannon entropy was used as a measure (in natural log units, or ‘nats’) of the available information content of each series (Shannon, 1948).

$$\mathbf{H}(x)=-\sum p_s\ln p_s,s\in S.$$ (6)

S is the set of possible symbols s, or possible rating values in ordinal variable x. In the case of the ordinal affect items, ratings were integers s ∈ {1, …,9}. A key property of entropy is that it is maximal when P (s ∈ S) is uniformly distributed. Entropy also increases with the number of possible symbols in S. Setting a minimum requirement for the total entropy across the set of variables ensures that at a minimum, either a few ratings were used on several items or several ratings were used on a few items. The entropy of a uniform distribution of 3 symbols is 1.1, so the total entropy for 7 of such items would be 7.7.

Simulations were used (See Appendix) to determine the statistical power resulting from values of N and T, given optimal H (x). Only 67 participants had H(x)⩾7.7. Of the participants that qualified, the average number of completed affect reports was about 64. Assuming maximal H(x), the resulting sample would have only a 43% chance of detecting an effect of if the true parameters of the negative binomial model were a dispersion of.2 and mean δ effect of −3. Choosing a lower entropy threshold, H(x) = 6.0 resulted in a potentially better balance of data quality with sample size (N= 94, 𝔼 [T] = 65), increasing our estimate of the maximum possible statistical power to 56%. Further decreases in the minimum H(x) were expected to add only highly noisy estimates of δ that no longer yield benefits to the statistical power. The complete set of data qualifications was therefore:

$$\sum _{i=1}^K{\mathbf{H}}_{\text{Wave}}\left(x_i\right)>6.0,T_{\text{Wave}}⩾6,T_{\text{Total}}⩾18.$$ (7)

The quality control metrics, total entropy and total complete rows of data per person, were regressed on demographic variables sex, age, race, mean latitude, mean longitude to determine whether data quality control procedures may bias the results. No significant nor apparently trending associations were found, suggesting that the informativeness of response patterns was largely idiosyncratic with respect to the available data.

3. Results

Results of the negative binomial regressions are shown in Table 2. Emotion regulation δ and affect sum score means μ_SS were most consistently significant (p < .05) across models, both uniquely and conditional on use with other predictors. After exponentiation, the significant effect sizes from the combined regression are interpreted as follows: Across participants, a 10% increase in emotion regulation rate corresponded to a 6–39% reduction in nicotine use, a 2–42% reduction in alcohol use, and a 2–34% reduction in cannabis use. A unit increase in mean negative affect sum score corresponded to a 7–31% increase in nicotine use, a 1–27% increase in alcohol use, and a 2–23% increase in cannabis use. Additionally, a unit standard deviation increase in negative affect sum scores corresponded to a 10–50% decrease in nicotine use. The true directions of causation responsible for these associations cannot be determined by this cross-sectional approach, so we present these effects only as the functional mappings given by the models. Negative affect sum score standard deviations were not significant for alcohol or cannabis in the combined model. Volatility, σ_w, was not significant, though with small p-values for cannabis and nicotine, it is possible that effects would be detectable in a larger sample.

Table 2.

Multiple Negative Binomial regression of substance use counts on: (a) only descriptive statistics of affect sum scores: mean (μ_SS) and standard deviation (σ_SS); (b) only model-based predictors: regulation (δ) and volatility (σ_w); (c) both descriptive and model-based statistics. β₀ is the intercept for each model.

		(a) Descriptive			(b) Model-based			(c) Combined
		Effect	CI	p	Effect	CI	p	Effect	CI	p
Nicotine	β0	−2.19	(−5.41, 1.04)	0.18	1.65	(0.77, 2.52)	0.00021	−1.34	(−4.71, 2.02)	0.43
	μSS	0.16	(0.06, 0.27)	*0.0017				0.17	(0.07, 0.27)	*0.0011
	σSS	−0.38	(−0.69, −0.06)	*0.019				−0.42	(−0.72, −0.11)	*0.0071
	δ				−2.71	(−4.88, −0.54)	*0.014	−2.85	(−5.02, −0.68)	*0.0099
	σw				5.87	(−5.05, 16.79)	0.29	8.86	(−1.46, 19.19)	0.092
Alcohol	β0	−2.58	(−6.41, 1.25)	0.19	0.67	(−0.31, 1.65)	0.18	−1.73	(−5.68, 2.22)	0.39
	μSS	0.12	(0, 0.24)	0.05				0.12	(0.01, 0.24)	*0.041
	σSS	−0.22	(−0.58, 0.14)	0.24				−0.25	(−0.6, 0.1)	0.16
	δ				−2.59	(−5.14, −0.04)	*0.046	−2.84	(−5.47, −0.2)	*0.035
	σw				3.55	(−9.4, 16.49)	0.59	6.98	(−5.43, 19.39)	0.27
Cannabis	β0	−2.79	(−5.81, 0.22)	0.069	0.95	(0.19, 1.71)	0.014	−2.42	(−5.6, 0.76)	0.14
	μSS	0.11	(0.02, 0.2)	*0.019				0.12	(0.02, 0.21)	*0.012
	σSS	−0.04	(−0.31, 0.23)	0.78				−0.05	(−0.32, 0.21)	0.71
	δ				−2.18	(−4.11, −0.26)	*0.026	−2.16	(−4.14, −0.18)	*0.033
	σw				7.48	(−1.95, 16.91)	0.12	8.92	(−0.48, 18.33)	0.063

Total R² values of each model are given in Table 3. Descriptive sum score statistics were the most predictive for nicotine, explaining 28% of variance in its use. By comparison, the model-based emotion regulation and volatility only explained 10% when used as the sole predictors. Similar proportions of the variance of alcohol and cannabis use were explained by either approach, with 15% for alcohol and 11% for cannabis. The variance explained by all predictors used in tandem was slightly greater than the sum of their separate models, possibly owing to the approximate nature of the generalized R² measure. Subtracting the R² of the descriptive statistics model from the R² of the combined model reveals that the variance explained by the novel, model-based predictors was independent from the variance explained by descriptive statistics. The descriptors were correlated with model-based indices between 0 and −.2, small enough to arise from sampling variation and insufficient to suggest methodological redundancy.

Table 3.

Generalized R² values for models predicting with: (a) only descriptive statistics of affect sum scores (mean and standard deviation); (b) only model-based statistics (regulation and volatility); (c) all four predictors; and (c)-(a), the improvement to R² as a result of including the model-based predictors with descriptors.

Model	Predictors	Nicotine	Alcohol	Cannabis
(a) Descriptive Only	μSS, σSS	0.28	0.15	0.11
(b) Model-based Only	δ, σw	0.10	0.14	0.11
(c) Both	μSS, σSS, δ, σw	0.42	0.31	0.23
(c)-(a) R2 improvement		0.14	0.16	0.12

4. Discussion

The results of our analyses demonstrate that the model-based index of emotion regulation predicted substance use independently of simpler descriptive statistics. The unique associations of each predictor were comparable in magnitude and explained a moderate to large proportion of variance in nicotine use when combined in the linear model. Less variance was explained in alcohol usage, and even further less in cannabis. These effects roughly follow the observed frequencies of each drug in these data, leading us to reserve judgment for larger and more general samples.

Causal interpretations of our results should be considered with caution and skepticism. The most likely scenario is that bidirectional feedback cycles occur between affective state and the decision to use a drug. The association of higher average negative affect with nicotine may reflect a tendency to smoke when coping with unpleasant emotions. Conversely, the association of lower standard deviations of mood with nicotine may be due to the damping effects of nicotine on emotional variability. The regulation and volatility indices were estimated irrespective of how these causal sequences were ordered, and thus suffer from the same ambiguity. Does substances use produce larger dynamic disturbances, or vice versa? Is substance use undertaken as a surrogate for intrinsic emotion regulation? One possibility is that individuals who show higher emotion regulation, (i.e., more rapid return to their baseline affect state after disturbances) might be less motivated to use substances as a coping strategy regardless of their mean affect level. Such individuals might have a larger repertoire of adaptive coping strategies to help them deal with everyday stressors. Elaborated process models can be specified to include the reciprocal causation between emotional states and the choice to use a drug, further distinguishing between the above scenarios. For instance, the following model extends Eq. (1) to include both direct effects and changes in regulation as a consequence of substance use:

$$\begin{gathered} \frac{d{x}_t}{dt}=\left({\lambda }_0+{\lambda }_1{\psi }_t\right)x_t+\beta {\psi }_t+w_t, \\ w\sim N\left(0,{\sigma }_{w,0}+{\sigma }_{w,1}{\psi }_t\right), \end{gathered}$$ (8)

where ψ_t may be a vector of indicators or quantities of different drugs. λ1 therefore determines the extent to which the substances impact emotion regulation, σ_w,1 indicates the same for emotional sensitivity, and direct, and direct, immediate effects on affect are scaled by β. In the current study, substance use was recorded as a binary variable, requiring it to be mapped to a continuously varying probability of occurrence, or liability. If we take ϕ_t as a dynamical state representing that liability, then that may be in turn modeled as responsive to affect:

$$\frac{d{\varphi }_t}{dt}=\gamma x_t+\zeta {\varphi }_t.$$ (9)

In this model, γ would determine the direction and rate that the liability changes with affect state, while ζ controls how long the liability lingers regardless of further changes in affect. These parameters could therefore serve as indices for individual liability to addiction based on emotional feedbacks.

For the purposes of this study, we only present these ideas as a motivating vignette. To successfully fit this kind of complex process model with empirical data, the data must meet certain standards of quantity and information content for statistical power and parameter identification. As we have shown, the available data did not meet a number of those standards. The majority of participants had either zero or few instances of substance use, uninformative response patterns on affect questionnaires, and frequently insufficient within-person sample sizes, leading us to make more conservative choices about model complexity. Our simplified modeling approach and aggregation techniques were chosen to allow comparison across as many individuals from the sample as possible despite that the majority them did not report more than a few occasions with a particular drug. Future studies aiming to fit a reciprocal feedback model like Eqs. (8) and (9) will require consistent, high-frequency sampling of both affect and substance use. Measured occasions of substance use should be interspersed by occasions without use so that the subsequent patterns specific to affect can be observed. Consequently, a study design should sample at least two or three times the expected frequency of substance use or else include event-contingent sampling strategies. If the parameters of the above model are used as indices in second-level analysis, as we did here, then statistical power will depend on the ratio of parameter standard error to true between-person variation in parameter values. We used simulations, described in the appendix, to compute power for our current, simplified modeling strategy. Further analyses and power calculations for reciprocal feedback models are beyond the scope of our current aims and are left for a subsequent study.

EMA studies involve many complex psychometric assumptions and analytic challenges. We attempted to address as many of the most common problems as possible, though solutions are necessarily subject to discretion. One of the primary goals of our study was therefore to demonstrate several effective methods of handling problems with EMA affect data, including irregular response intervals, uninformative response patterns, and questionnaire aggregation. With these strategies come basic limitations.

First, as our power calculations showed, the resulting analysis only had approximately a 56% chance of detecting a moderate effect of emotion regulation on substance use. The primary concern with low power is the inability to detect other important effects. Emotional volatility in all three substances consistently had small, near-significant effects that may be observable in a larger sample. The same power-calculation simulations showed that 80% power at α = .05 for the current analysis could be achieved with at least 250 participants with 30 time points each or 130 participants with at least 115 time points each.

One possible criticism may be aimed at our use of entropy for quality control. We used the power analysis and analytic reasoning to present a general estimate of how our results would change, but ultimately the chosen threshold for entropy is neither strict nor final. Exact calculations that account for the information content of each series would allow calibration of the minimum entropy based on the false positive rate. Because our power calculations do not account for uninformative response patterns, we consider the resulting estimate as a best case scenario.

It also is not certain whether the outcome of our quality control criteria was entirely random. Because the study participants were underage adolescents, it is possible that many individuals who used substances during the study period did not report their usage or other psychological information to avoid possible social and legal consequences. The under-reporting quantified by our methods, either as missing data or uninformative data, may have been even more likely for the most severe cases of substance use. Indeed, the majority of participants did not produce sufficiently informative data, so we must therefore condition our conclusions on an above-average willingness to cooperate with the study and a certain perceived security in doing so.

Another possible criticism regards the use of ”safe” as an affect indicator. The question was worded as “How safe are you right now?” leaving some ambiguity in whether responses indicated feelings of safety or rational assessments of the current environment. In the latter case, it may not be appropriate to include among the other affect indicators. Table 1 shows that it was strongly correlated with the other indicators. Under a latent variable measurement model, we assume that it is correlated with the other indicators because each represents in common an underlying phenomenon, namely negative affect. From the alternative perspective of such indicators as a directional network, it may indeed be a rational assessment of the environment from which the other reported subjective experiences follow as a consequence. It is difficult to compare the validity of network and latent variable methods in a general way, and alternative approaches to multivariate affect may yield unique and important insights. We relied on a latent variable or dimension-reduction approach and the assumption that “safety” corresponded to a subjective experience because altogether, the combined information of the ordinal indicators produced a smooth series with a nearly continuous sample space that is more amenable to state-space modeling. The entropy of the safety measure in particular was greater on average than the other indicators, which suggests that it was easier for the participants to interpret and evaluate in a detailed way. Under either interpretation, as a subjective feeling or an evaluation of the situation, safety likely increased the association with substance use because the data were collected in adolescents below the legal age for the consumption of alcohol or nicotine. Acquiring and using drugs likely required engaging in other unsafe situations.

4.1. Conclusions

The current study examined the utility of a theoretically conceived measure of emotional variability that describes individual tendencies toward homeostasis, i.e., emotion regulation. Our results showed that emotion regulation was uniquely and independently associated with substance use in high-risk adolescents. Using model-based indices lends to the development of more specific theoretical hypotheses as compared to generic descriptive indices. Combined use of theoretical and descriptive indices appears to provide the greatest predictive utility. Further work is warranted to determine the nature of the observed associations between emotion regulation and substance use.

HIGHLIGHTS.

• Repeated self-reported assessments of affect taken in Experience Sampling designs may show patterns of variation that reveal underlying properties of feedback control.

• Substance use may result from, supplant, or disrupt normal patterns of emotion regulation.

• A feedback-control state-space model of emotional homeostasis was used to produce an index of emotion regulation from affect time series.

• The model-based measure of emotion regulation was associated with substance use independently from simple descriptive statistics, adding complementary predictive value.

Appendix A. Power analysis

Simulations were used to obtain approximate estimates of the statistical power of the two-step analysis. The following steps were taken to create a model of power given number of people in the sample (N) and average timepoints per person (T). First, a random, Gaussian distribution of N autoregressive coefficients (β) was generated. N random values representing substance use counts were then generated from a negative binomial distribution with parameters dispersion of.2 and mean of 3β. Negative binomial parameter values were chosen such that the descriptive statistics and visual inspection approximated the joint distributions of estimated β_i and substance use counts from the data. Autoregressive time series of length T were generated by convolving (convolve() with argument type=“open”) the cumulative sum of a white noise variable of length T with the transfer function ${\mathbf{e}}^{ln\left({\beta }_i\right)t}$ values out to length 150, and trimming 150 points from the beginning and end of the resulting convolution. R functions ar() and glm.nb() from package MASS (Venables & Ripley, 2002) were used to estimate β from the data and regress substance use counts upon the estimated β, respectively. The simulation-estimation routine was carried out for 500 trials per condition, with conditions defined as

$$N=2^k,k\in [5,5.5,6,6.5,\dots \mathrm{..8}],$$

and

$$T=2^{5k},k\in [2,2.5,3,3.5,\dots \mathrm{..8}].$$

For each condition, a true positive rate was calculated as the total percentage of results meeting statistical significance at p < .05. The percentage was then regressed upon each corresponding N^j and T ^j with j ∈ [1, 2, 3, 4], producing a quartic linear model of statistical power.

The model was used in the study to calculate approximate power for the two-step analysis from inputs N and T.