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The transition from childhood to adolescence is a crucial period for the development of healthy behaviors to be sustained later in life. With obesity a leading public health problem, the promotion of healthy behaviors has the potential to make a huge impact. The current study evaluated Stage of Change progression in a large (N = 4158) computer-delivered, Transtheoretical Model-tailored intervention focusing on physical activity and fruit and vegetable consumption (FV). Markov models were used to explore stage transitions and patterns of discrete change from sixth to ninth grade. Nested model comparisons examined the consistency of these patterns across time and intervention condition. Major findings supported models in which participants were free to transition forward and backward to any of the stages, but higher probabilities were observed for remaining in the same stage or for transitioning one or two stages forward. Participants in the intervention group had higher probabilities of transitioning toward Maintenance, with more change occurring relative to the comparison group during transitions from grades six to eight but not for grades eight to nine.

Little is known about the extent to which interrupted time series analysis (ITSA) can be applied to short, single-case study designs and whether those applications produce results consistent with visual analysis (VA). This article examines the extent to which ITSA can be applied to single-case study designs and compares the results based on two methods: ITSA and VA, using papers published in the Journal of Applied Behavior Analysis in 2010. The study was made possible by the development of software called UnGraph®, which facilitates the recovery of raw data from the graphs. ITSA was successfully applied to 94% of the examined graphs with the number of observations ranging from 8 to 136. Moderate to high lag-1 autocorrelations (>.50) were found for 46% of the data series. Effect sizes similar to group-level Cohen's d were identified based on the tertile distribution. Effects ranging from 0.00 to 0.99 were classified as small, those ranging from 1.00 to 2.49 as medium, and large effect sizes were defined as 2.50 or greater. Comparison of the conclusions from VA and ITSA had a low level of agreement (Kappa =.14, accounting for the agreement expected by chance). The results demonstrate that ITSA can be broadly implemented in applied behavior analysis research. These two methods should be viewed as complementary and used concurrently.

To improve complex behaviors such as adherence to medical recommendations, a better understanding of behavior change over time is needed. The focus of this study was adherence to treatment for obstructive sleep apnea (OSA). Adherence to the most common treatment for OSA is poor. This study involved a sample of 161 participants, each with approximately 180 nights of data. First, a time series analysis was performed for each individual. Time series parameters included the mean (average hours of use per night), level, slope, variance, and autocorrelation. Second, a dynamic cluster analysis was performed to find homogenous subgroups of individuals with similar adherence patterns. A four-cluster solution was found, and the subgroups were labeled: Great Users (17.2%; high mean and level, no slope), Good Users (32.8%; moderate mean and level, no slope), Low Users (22.7%; low mean and level, negative slope), and Slow Decliners (moderate mean and level, negative slope, high variance). Third, participants in the identified subgroups were compared to establish external validity. These steps represent a Typology of Temporal Patterns (TTP) approach. Combining time series analysis and dynamic cluster analysis is a useful way to evaluate longitudinal patterns at both the individual level and subgroup level.

Testing Theory-based Quantitative Predictions (TTQP) represents an alternative to traditional Null Hypothesis Significance Testing (NHST) procedures and is more appropriate for theory testing. The theory generates explicit effect size predictions and these effect size estimates, with related confidence intervals, are used to test the predictions. The focus of a study is shifted to a quantitative approach in contrast to the NHST dyadic decision centered on testing a prediction not based on the theory. This article describes the TTQP as an alternative approach by replicating and extending a test of 40 a priori predictions based on the Transtheoretical Model (TTM). Specific quantitative predictions were made about the magnitude of the effect size (ω(2)). The predictions involved movement from 1 of 3 initial stages (Precontemplation, Contemplation, and Preparation) to stage membership 12 months later. In the initial study, 36 of the 40 predictions were confirmed. The same 40 predictions are evaluated on a sample (N = 3,923) of smokers recruited from a large New England HMO for a smoking cessation study. The predictions were recalibrated based on the first study and 99% confidence intervals were employed to test the predictions. Thirty-two of the 40 predictions were confirmed. Of the 8 failures, 4 were judged to reflect a need for further recalibration, 1 was attributed to sampling fluctuation, and 3 suggested revisions of the theory are needed. The results provide overall support for the TTM. The study also illustrates some of the challenges of testing quantitative predictions.

Increasing adherence to medical recommendations is crucial for improving health outcomes and reducing costs of health care. To improve adherence, we have to better understand behavior change over time. The focus of this study was adherence to treatment for obstructive sleep apnea (OSA). Adherence to positive airway pressure (PAP), the most common treatment for OSA, is poor. This study involved an international sample of 161 participants, each with approximately 180 nights of data, and had three phases. First, a separate time series analysis was performed for each individual. Time series parameters included the mean (average hours of use per night), level (the intercept), slope (the rate of change over time), variance (variability in use), and autocorrelation (a measure of dependency). Second, a dynamic cluster analysis was performed to find homogenous subgroups of individuals with similar adherence patterns. A four-cluster solution was found, and the subgroups were labeled (see Figure 1 ): Great Users (17.2%; high mean and level, no slope), Good Users (32.8%; moderate mean and level, no slope), Poor Users (22.7%; low mean and level, negative slope), and Slow Decliners (moderate mean and level, negative slope, high variance). Third, participants in the identified subgroups were compared on a number of variables that were not involved in the clustering to establish external validity. Some notable findings at later time points include the following: Great Users reported the most self-efficacy (confidence to use PAP), Poor Users reported the most sleepiness, and Great Users reported the highest quality of sleep. Combining time series analysis and dynamic cluster analysis is a useful way to evaluate adherence patterns at both the individual level and subgroup level. Psychological variables relevant to adherence patterns, such as self-efficacy, could be the focus of interventions to increase PAP usage.

The effects of overextracting factors and components within and between the methods of maximum likelihood factor analysis (MLFA) and principal component analysis (PCA) were examined. Computer-simulated data sets were generated to represent a range of factor and component patterns. Saturation (aij = .8, .6 & .4), sample size (N = 75, 150,225,450), and variable-to-component (factor) ratio (p:m = 12:1,6:1, & 4:1) were conditions manipulated. In Study 1, scores based on the incorrect patterns were correlated with correct scores within each method after each overextraction. In Study 2, scores were correlated between the methods of PCAand MLFA after each overextraction. Overextraction had a negative effect, but scores based on strong component and factor patterns displayed robustness to the effects of overextraction. Low item saturation and low sample size resulted in degraded score reproduction. Degradation was strongest for patterns that combined low saturation and low sample size. Component and factor scores were highly correlated even at maximal levels of overextraction. Dissimilarity between score methods was the greatest in conditions that combined low saturation and low sample size. Some guidelines for researchers concerning the effects of overextraction are noted, as well as some cautions in the interpretation of results.

Cross-sectional time series designs assess the generalizability of intervention effects across different units. The general transformation approach to time series analysis was proposed by Velicer and McDonald (1984) to avoid the model identification step. A general transformation matrix is employed for all analyses rather than the specific matrix associated with a particular model. This article extends the general transformation matrix approach to the analysis of multiple unit data by the development of a patterned transformation matrix. A sequence of tests of the parameters permits the assessment of between unit differences. The resulting procedure includes several alternative approaches as special cases and is easily implemented with only minor revisions in existing computer software.

Patterns of change occurring in a combined cross-sectional and longitudinal (cross-sequential) analysis of 14 variables were investigated in a two-year study of self-change approaches to smoking cessation. Every six months for five rounds, subjects (N = 544) were assessed on 10 change processes, self-efficacy, temptations to smoke, and their decisions weighing the pros and cons of smoking. Subjects were also assessed on which of the following four stages of change they were in at each round: precontemplation, contemplation, action and maintenance. Dynamic clustering was employed to group subjects on the basis of their patterns of changes in stages over the five rounds. This yielded 14 profile groups (longitudinal typologies) which initially were compared on the 14 variables. Patterns of change on each of the variables became clear when the data were integrated cross-sectionally and longitudinally to form composite developmental profiles. The basic pattern of change processes can best be represented by a mountain metaphor. The change processes followed a general pattern of increasing from precontemplation to contemplation, peaked at a particular stage of change and then declined either to precontemplation levels or to somewhat higher levels if used as relapse prevention strategies. Temptation and the pros of smoking followed a linear pattern of decreasing across the stages, while self-efficacy increased linearly. The patterns of change and the mountain metaphor can be used as an organizing principle for developing models of change. The models can be used to develop therapy programs and self-help programs based on how people change their own problem behavior.

Interrupted time series analysis involves repeated observations on a single unit both preceding and following an intervention. Recently developed statistical procedures permit inferential statements about the degree and pattern of the intervention effect. Five different software packages appropriate for interrupted time series analysis were evaluated: TSX, GENTS, BMDP, SAS, and ITSE. Simulated data was generated from 44 types of series representing eleven different ARIMA models, two types of intervention, and two different series' lengths. The five programs are compared with respect to the accuracy of estimation of the error variance, pre-intervention level, post-intervention level, and slope estimates (where appropriate). Three programs produced generally satisfactory results (TSX, GENTS, and SAS), one was generally inaccurate across a wide range of models (ITSE), and one produced some inaccuracies and occasionally failed to complete the analysis (BMDP).

Interrupted time series analysis is a method of analysis for longitudinal experiments involving a sequence of observations on a single dependent variable before and after an intervention. The presence of dependency in the data necessitates the use of computer programs for data analysis. Five recently developed programs are evaluated: BMDP (Dixon, 1985), GENTS (Velicer, Fraser, McDonald, & Harrop, 1980), ITSE (Williams & Gottman, 1982), SAS (SAS Institute, 1984), and TSX (Bower & Glass, 1974). Characteristics evaluated include computational features, quality of documentation, and CPU time required.

Should one do a component analysis or a factor analysis? The choice is not obvious, because the two broad classes of procedures serve a similar purpose, and share many important mathematical characteristics. Despite many textbooks describing common factor analysis as the preferred procedure, principal component analysis has been the most widely applied. Here we summarize relevant information for the prospective factor/component analyst. First, we discuss the key algebraic similarities and differences. Next, we analyze a number of theoretical and practical issues. The more practical aspects include: the degree of numeric similarity between solutions from the two methods, some common rules for the number of factors to be retained, effects resulting from overextraction, problems with improper solutions, and comparisons in computational efficiency. Finally, we review some broader theoretical issues: the factor indeterminacy issue, the differences between exploratory and confirmatory procedures, and the issue of latent versus manifest variables.

Computer generated data representative of 26 ARIMA models was used to compare the results of interrupted time-series analysis using: (1) the known model identification, (2) an assumed (1, 0, 0) model, and (3) an assumed (3, 0, 0) model as an approximation to the General Transformation approach. Ten samples each of 26 ARIMA processes were generated representing ARIMA (0, 0, 0), (0, 0, 1), (1, 0, 0), (0, 1, 0), and (0, 1, 1) models with varying degrees of dependency. Series were generated with both 40 points and 100 points, with an immediate and constant intervention effect of magnitude one (occurring at the midpoint), and with a random error component variance of magnitude one. The results of the three analyses are compared to the criterion values and to each other for the point estimates of: l) the minimum residual error variance; 2) the pre-intervention level; and 3) the post-intervention change in level. The results for models which included a difference parameter were inaccurate for all three approaches. All three analyses provided reasonable and equivalent results for the remaining or non-differencing models for series with both 40 and 100 points The findings strongly suggest that the problematic model identification process might be eliminated entirely and replaced with the assumed (1, 0, 0) approach or the General Transformation approach.

The performance of four rules for determining the number of components to retain (Kaiser's eigenvalue greater than unity, Cattell's SCREE, Bartlett's test, and Velicer's MAP) was investigated across four systematically varied factors (sample size, number of variables, number of components, and component saturation). Ten sample correlation matrices were generated from each of 48 known population correlation matrices representing the combinations of conditions. The performance of the SCREE and MAP rules was generally the best across all situations. Bartlett's test was generally adequate except when the number of variables was close to the sample size. Kaiser's rule tended to severely overestimate the number of components.

Factor analysis, image component analysis, and principal component analysis are three methods that have been employed for the same purpose. Factor analysis was traditionally viewed as the preferred method, with other methods serving as computationally easier approximations. Recently attention has been focused on theoretical problems with the factor analysis model such as the factor indeterminacy issue. In order to assess the degree of similarity between the results produced by each of the three methods, the patterns produced by maximum likelihood factor analysis, rescaled image analysis, and principal component analysis are compared for nine data sets. Two different comparisons are considered: a direct loading-by-loading comparison of the patterns, and a summary statistic defined on the matrix of differences between patterns. Comparisons are made for the patterns in both orthogonal and oblique rotational positions, and a position of maximum similarity is achieved by an orthogonal procrustes rotation. The patterns produced by each of the three methods were remarkably similar. Image component analysis and maximum likelihood factor analysis generally produced the most similar results and principal component analysis and maximum likelihood factor analysis generally produced the most dissimilar results. Differences generally occurred in the last factor extracted, possibly because too many factors had been extracted.

Factor analysis and component analysis represent two broad classes of methods employed generally with similar types of problems. The purpose of the present study is to determine the extent to which and under what conditions the methods produce different patterns. Principal component analysis, image component analysis, and maximum likelihood factor analysis were performed on simulated data matrices. Comparisons were made between each of the three methods and to ideal patterns. Sample size, saturation, and type of pattern were systematically varied. The general conclusion reached is that the three methods produce results that are equivalent. In addition, several important trends were observed.

An attribution of a latent variable procedure, such as factor analysis, that is sometimes cited is superior generalization from the variables sampled to the population of variables. Principal component analysis, image component analysis, and maximum likelihood factor analysis were compared to assess the effects of variable sampling. Three other independent variables were manipulated: (a) the size of the loadings or saturation, (b) the average number of variables per factor, and (c) the number of variables sampled. Five different correlation matrices were generated for each condition. Ten different variable samples were randomly selected. The sample pattern was then compared to the appropriate population pattern. The effects of method of analysis were relatively minor and very complex. The results with respect to degree of saturation and average number of variables per factor were clear and dramatic. Differential effects on boundary cases and nonconvergence problems were also found.

Time series analysis is a method for analyzing repeated observations on a single unit. Previously developed approaches involve a two stage process: (1) identifying which of various ARIMA (p,d,q) models best describe the underlying process; and (2) on the basis of the identified model, transforming the observed data to meet the assumptions (i.e., independence of data) of the general linear model, and estimating and testing the intervention effects. The present paper explores employing a general transformation to avoid the model identification step. This approach permits the employment of time series analysis in a wider variety of situations as a result of relaxing the requirement of a large number of points for model identification. The generalized transformation approach permits alternative computational procedures, based on a generalized least squares algorithm, that has greater flexibility and efficiency.