Tenets and Methods of Fractal Analysis (1/f Noise).

This chapter deals with the methodical challenges confronting researchers of the fractal phenomenon known as pink or 1/f noise. This chapter introduces concepts and statistical techniques for identifying fractal patterns in empirical time series. It defines some basic statistical terms, describes two essential characteristics of pink noise (self-similarity and long memory), and outlines four parameters representing the theoretical properties of fractal processes: the Hurst coefficient (H), the scaling exponent (α), the power exponent (ß), and the fractional differencing parameter (d) of the ARFIMA (autoregressive fractionally integrated moving average) method. Then, it compares and evaluates different approaches to estimating fractal parameters from observed data and outlines the advantages, disadvantages, and constraints of some popular estimators. The final section of this chapter answers the questions: Which strategy is appropriate for the identification of fractal noise in empirical settings and how can it be applied to the data?

Temporal Relationships Between Abdominal Pain, Psychological Distress and Coping in Patients With IBS - A Time Series Approach.

Objective: Irritable bowel syndrome (IBS) is a chronic disease leading to abdominal pain that is often related to psychological distress. The aim of the study was to investigate the temporal relationships between abdominal pain and psychological variables in patients with IBS. Methods: This longitudinal diary study included eight patients from a waiting group, recruited in the frame of a pilot intervention study. During their waiting time of 3 months the patients answered questions daily regarding somatic and psychological variables using an online diary. All patients were considered and analyzed as single cases. The temporal dynamics between the time series of psycho-somatic variables were analyzed using a vector autoregressive (VAR) modeling approach. Results: For all patients, positive same-day correlations between somatic and psychological time series were observed. The highest same-day correlations were found between somatic symptoms and pain-related discomfort (r = 0.40 to r = 0.94). Altogether, n = 26 significant lagged relationships were identified; n = 17 (65%) indicated that somatic values were predictive of psychological complaints on the following days. N = 9 (35%) lagged relationships indicated an opposite relationship in that psychological complaints were predictive of somatic symptoms. Three patients showed a significant positive same-day correlation between abdominal pain and use of a positive coping strategy. However, significant lagged relationships in two patients showed that for these patients the use of positive thinking as a coping strategy was unhelpful in reducing pain on the following days. Conclusions: In patients with IBS abdominal symptoms appear to be closely related to psychological symptoms. For some patients, somatic complaints predict psychological complaints, in other patients the directionality is opposite. The impact of coping strategies on somatic symptoms varies among patients, therefore their role for a possible reduction of pain should be further explored. The results suggest the need of characterizing patientsindividually for effective health interventions. Individual time series analyses provide helpful tools for finding reasonable person-level moderators.

Pain and psyche in a patient with irritable bowel syndrome: chicken or egg? A time series case report.

BACKGROUND: Irritable bowel syndrome (IBS) appears to have a bidirectional interaction with both depressive and anxiety-related complaints. However, it remains unclear how exactly the psychological complaints, at the individual level, are related to somatic symptoms on a daily basis. This single case study investigates how somatic and psychological variables are temporally related in a patient with irritable bowel syndrome. CASE REPORT: The patient was a woman in her mid-twenties with an IBS diagnosis. She reported frequent soft bowel movements (5-6 times per day), as well as flatulence and abdominal pain. She resembled a typical IBS patient; however, a marked feature of the patient was her high motivation for psychosomatic treatment as well as her willingness to try new strategies regarding the management of her symptoms. As an innovative approach this single case study used a longitudinal, observational, time series design. The patient answered questions regarding somatic and psychological variables daily over a period of twelve weeks with an online diary. The diary data was analysed using an autoregressive (VAR) modeling approach. Time series analyses showed that in most variables, strong same-day correlations between somatic (abdominal pain, daily impairment) and psychological time series (including coping strategies) were present. The day-lagged relationships indicated that higher values in abdominal pain on one day were predictive of higher values in the psychological variables on the following day (e.g. nervousness, tension, catastrophizing, hopelessness). The use of positive thinking as a coping strategy was helpful in reducing the pain on the following days. CONCLUSION: In the presented case we found a high correlation between variables, with somatic symptoms temporally preceding psychological variables. In addition, for this patient, the use of positive thoughts as a coping strategy was helpful in reducing pain.

Time series analyses with psychometric data.

Understanding of interactional dynamics between several processes is one of the most important challenges in psychology and psychosomatic medicine. Researchers exploring behavior or other psychological phenomena mostly deal with ordinal or interval data. Missing values and consequential non-equidistant measurements represent a general problem of longitudinal studies from this field. The majority of process-oriented methodologies was originally designed for equidistant data measured on ratio scales. Therefore, the goal of this article is to clarify the conditions for satisfactory performance of longitudinal methods with data typical in psychological and psychosomatic research. This study examines the performance of the Johansen test, a procedure incorporating a set of sophisticated time series techniques, in reference to data quality utilizing a Monte Carlo method. The main results of the conducted simulation studies are: (1) Time series analyses require samples of at least 70 observations for an accurate estimation and inference. (2) Discrete data and failing equidistance of measurements due to irregular missing values appear unproblematic. (3) Relevant characteristics of stationary processes can be adequately captured using 5- or 7-point ordinal scales. (4) For trending processes, at least 10-point scales are necessary to ensure an acceptable quality of estimation and inference.

How to Deal With Temporal Relationships Between Biopsychosocial Variables: A Practical Guide to Time Series Analysis.

OBJECTIVE: Longitudinal data allow for conclusions about the temporal order of events and interactional dynamics between several processes. The aim of this article is to provide a concise and pragmatic description of time series analyses (TSAs) of patient samples with numerous (or daily) repeated biological, behavioral, or psychological measurements. In addition, the article demonstrates how to implement the described analyses with the software R. METHODS: To illustrate the concrete application of the time series method, we use two case series of patients with anorexia nervosa. Upon awakening, the patients collected salivary cortisol on a daily basis and answered several questions on a handheld computer (electronic diary) regarding psychosocial variables at the time of salivary collection. RESULTS: Basic concepts of time series analysis such as stationarity, auto- and cross-correlation, Granger causality, impulse response function, and variance decomposition are presented. In addition, we demonstrate vector autoregressive analyses with three variables. For Patient 1, we demonstrate how TSA is used to detect cortisol and anxiety decreases during inpatient treatment and also how TSA can be used to show that an increase in cortisol is followed by a next-day increase in anxiety. For Patient 2, TSA was used to show higher salivary cortisol upon awakening on the days the patient was weighed compared with other days. In addition, we show how interdependencies of depressive feelings, positive anticipations, and cortisol values can be quantified using TSA. CONCLUSIONS: Time series designs enable modeling of temporal relationships and bidirectional associations between biopsychosocial variables within individuals. These individual patterns cannot be derived from traditional group-based statistical analyses. This article provides accessible research tools for conducting TSA relevant to psychosomatic and biobehavioral research.

[Process analysis of weekly self- and external assessments of adolescents with substance abuse disorder during long-term psychotherapy]. / Verlaufsanalyse wöchentlicher Selbst- und Fremdeinschätzungen in der Langzeittherapie suchtkranker Jugendlicher.

Process analysis of weekly self- and external assessments of adolescents with substance abuse disorder during long-term psychotherapy Abstract. OBJECTIVE: Little is known about the course of emotional and motivational states in young patients with substance use disorder (SUD) during long-term treatment. METHOD: We collected weekly self-reports from N = 42 adolescents, resulting in 853 questionnaires. Additionally, 708 observations were obtained from their key carers. Principal component analysis (PCA) was used to explore the dimensional structure of the questionnaires. Multi-level models were applied to test for group differences and time series models to evaluate dependencies on the person level. RESULTS: PCA yielded four factors: negative mental state, appreciation of the setting, motivation, and addiction dynamics. Correlations between self- and (unidimensional) carer-reports were low to moderate, but differential on the individual level. Scores of all four scales decreased during the course of treatment. The level of appreciation during the initial phase was the only significant predictor for drop-outs of treatment later on: in drop-outs, appreciation decreased, whereas it increased in completers. CONCLUSION: Appreciation was the most important predictive factor for a regular therapy ending in SUD, whereas motivation showed fluctuations typical for adolescence. Addiction dynamics were of lesser relevance than commonly expected. Therefore, programs in long-term SUD treatment should focus more on improving appreciation than on issues of addiction itself.

Emotional Intolerance and Core Features of Anorexia Nervosa: A Dynamic Interaction during Inpatient Treatment? Results from a Longitudinal Diary Study.

OBJECTIVE: The role of emotion dysregulation with regard to the psychopathology of anorexia nervosa (AN) is increasingly discussed. It is both assumed that AN symptoms have an impact on difficulties in tolerating aversive emotions and that-conversely-emotion dysregulation influences AN. To date, such conclusions are drawn on the basis of cross-sectional data not allowing for inferences on the temporal dynamics. The current study investigates the longitudinal interaction between emotional intolerance and core AN symptoms over the course of inpatient treatment by comparing patients with high (BMI<15 kg/m2) vs. low symptom severity (HSS vs. LSS). METHOD: The study adopted a longitudinal, process-oriented design with N = 16 analysed electronic diaries. Throughout the course of their inpatient treatment, the patients answered questions daily about emotional intolerance and their AN-specific cognitions and behaviours. The temporal dynamics between emotional intolerance and these variables were analysed using a multivariate time series approach. RESULTS: The time series of the processes under investigation adequately reflected the individual treatment courses. The majority of significant linear time trends was found for HSS patients. Most importantly, analysis revealed significant temporal interactions between emotional intolerance and AN symptoms in almost 70% of HSS patients. Thereby, up to 37% of variance in eating restraint and up to 23% in weight concern could be attributed to changes in emotional intolerance. CONCLUSIONS: The findings support the notion that intolerable unpleasant emotions in severely affected AN patients influence their psychopathology. Additionally, time series analysis outlined the inter-individual heterogeneity of psychosomatic treatment courses of AN patients.

Temporal relationships between awakening cortisol and psychosocial variables in inpatients with anorexia nervosa - A time series approach.

OBJECTIVE: The aim of the study was to investigate the characteristics of the awakening salivary cortisol in patients with anorexia nervosa (AN) using a time series design. We included ten AN inpatients, six with a very low BMI (high symptom severity, HSS group) and four patients with less severe symptoms (low symptom severity, LSS group). METHODS: Patients collected salivary cortisol daily upon awakening. The number of collected saliva samples varied across patients between n=65 and n=229 (due to the different lengths of their inpatient stay). In addition, before retiring, the patients answered questions daily on the handheld regarding disorder-related psychosocial variables. The analysis of cortisol and diary data was conducted by using a time series approach. RESULTS: Time series showed that the awakening cortisol of the AN patients was elevated as compared to a control group. Cortisol measurements of patients with LSS essentially fluctuated in a stationary manner around a constant mean. The series of patients with HSS were generally less stable; four HSS patients showed a non-stationary cortisol awakening series. Antipsychotic medication did not change awakening cortisol in a specific way. The lagged dependencies between cortisol and depressive feelings became significant for four patients. Here, higher cortisol values were temporally associated with higher values of depressive feelings. CONCLUSIONS: Upon awakening, the cortisol of all AN patients was in the standard range but elevated as compared to healthy controls. Patients with HSS appeared to show less stable awakening cortisol time series compared to patients with LSS.

Increasing fruit and vegetable intake. "Five a day" versus "just one more".

The present randomized controlled intervention study tested the hypothesis that a personally adaptable and realistic "just 1 more" goal would be more effective for increasing fruits and vegetables (FV) intake compared to the common "5 a day" goal. Study participants (N=84 students, 85% female) consumed less than 4 servings of FVs per day at recruitment. During the 1-week intervention, participants randomized to the 5 a day-group were asked to eat 5 servings of FVs/day; participants of the just 1 more-group were asked to eat 1 serving more of FVs than they usually did, and participants of the control group were instructed to eat as usual. Measurements were taken before (T1), directly following (T2), and 1 week after (T3) the intervention. Participants in the 5 a day-group increased their average FV intake significantly by about one serving from 2.49 at T1 to 3.45 servings/day at T3. At T3, only the 5 a day-group-not the just 1 more-group-had a significantly higher FV intake than the control group. Contrary to the hypothesis, the "5 a day" goal was more effective than "just 1 more" for increasing FV intake. Results of our study support the rationale of the "5 a day" campaign, at least in the short term.

Measuring fractality.

WHEN INVESTIGATING FRACTAL PHENOMENA, THE FOLLOWING QUESTIONS ARE FUNDAMENTAL FOR THE APPLIED RESEARCHER: (1) What are essential statistical properties of 1/f noise? (2) Which estimators are available for measuring fractality? (3) Which measurement instruments are appropriate and how are they applied? The purpose of this article is to give clear and comprehensible answers to these questions. First, theoretical characteristics of a fractal pattern (self-similarity, long memory, power law) and the related fractal parameters (the Hurst coefficient, the scaling exponent α, the fractional differencing parameter d of the autoregressive fractionally integrated moving average methodology, the power exponent ß of the spectral analysis) are discussed. Then, estimators of fractal parameters from different software packages commonly used by applied researchers (R, SAS, SPSS) are introduced and evaluated. Advantages, disadvantages, and constrains of the popular estimators ([Formula: see text] power spectral density, detrended fluctuation analysis, signal summation conversion) are illustrated by elaborate examples. Finally, crucial steps of fractal analysis (plotting time series data, autocorrelation, and spectral functions; performing stationarity tests; choosing an adequate estimator; estimating fractal parameters; distinguishing fractal processes from short-memory patterns) are demonstrated with empirical time series.

Some critical aspects of fractality research.

Numerous empirical studies identified fractal noise in human behavior. According to the theory of Self Organized Criticality, long memory 1/f scaling is a signature of stable and adaptive complex dynamical systems. This article discusses the following aspects of fractality research: (a) generation of fractal noise in simulation studies; (b) quality of some popular estimators of fractal parameters; (c) measurement artifacts in cognitive performances. 36 time series obtained in response tasks experiments under three different task conditions serve as empirical basis.