Mixed-model Design Research Articles

Robust Designs for Linear Mixed Effects Models

Summary In health sciences, medicine and social sciences linear mixed effects models are often used to analyse time-structured data. The search for optimal designs for these models is often hampered by two problems. The first problem is that these designs are only locally optimal. The second problem is that an optimal design for one model may not be optimal for other models. In this paper the maximin principle is adopted to handle both problems, simultaneously. The maximin criterion is formulated by means of a relative efficiency measure, which gives an indication of how much efficiency is lost when the uncertainty about the models over a prior domain of parameters is taken into account. The procedure is illustrated by means of three growth studies. Results are presented for a vocabulary growth study from education, a bone gain study from medical research and an epidemiological decline in height study. It is shown that, for the mixed effects polynomial models that are applied to these studies, the maximin designs remain highly efficient for different sets of models and combinations of parameter values.

Research and evaluation methods in special education

Preface Acknowledgments About the Authors 1. Introduction Questions and Activities for Application and Discussion 2. Program Evaluation Questions and Activities for Application and Discussion 3. Literature Review Purposes of the Literature Review Resources to Support the Literature Review Reporting the Literature Review Method Aggregating Information for a Literature Review The Integrated Literature Review Questions to Critically Analyze the Literature Review Questions and Activities for Application and Discussion 4. Quantitative Research Methods: Questions of Impact Philosophical Assumptions Associated With Quantitative Research Questions and Activities for Application and Discussion 5. Other Quantitative Approaches: Casual Comparative, Correlational, Single Case, and Survey Research Causal Comparative and Correlational Research Questions for Critically Analyzing Causal Comparative and Correlational Research Questions for Critically Anaylzing Single-Case Designs Survey Research Questions for Critically Analyzing Survey Research Questions and Activities for Application and Discussion 6. Qualitative Methods Definition and Characteristics of Qualitative Methods Importance of Qualitative Methods in Special Education Research Philosophical Assumptions and Methodological Implications in Special Education Research Qualitative Methods and Data Collection Strategies Critically Analyzing Qualitative Research Questions for Critically Analyzing Qualitative Research Questions and Activities for Application and Discussion 7. Mixed Methods and Mixed Model Designs Definitions and Characteristics Questions and Activities for Application and Discussion 8. Identification and Selection of Research Participants Population and Sample Definition Designing and Selecting Samples Generalizability, External Validity, and Transferability Ethics and Confidentiality Questions for Critically Analyzing Sample Design and Implementation Questions and Activities for Application and Discussion 9. Information Collection The Purpose of Information Collection Technical Adequacy of Data Collection Instruments Selecting and Using a Measurement Device Questions for Critically Analyzing Information Collection Strategies and Instruments Questions and Activities for Application and Discussion 10. Data Analysis, Interpretation, and Use Quantitative Data Anaylsis Challenges in Analysis and Interpretation Responses to Analysis and Interpretation Challenges Qualitative Data Analysis and Interpretation Reporting Research Beyond Reporting: Using Research Results Questions for Critically Analyzing Data Analysis and Interpretation Questions and Activities for Discussion and Application Appendices 1. Federal Definitions for Individuals with Disabilities 2. Data Sources from Extant Data Bases 3. Definitions of Statistical Terms 4. Funding Resources 5. Proposal Outline References Index

Upper quadrant postural changes of school children in response to interaction with different information technologies

The objective of this study was to quantitatively analyse the sitting posture of school children interacting with both old (book) and new (laptop and desktop computers) information technologies to test the hypothesis that posture is effected by the type of information technology (IT) used. A mixed model design was used to test the effect of IT type (within subjects) and age and gender (between subjects). The sitting posture of 32 children aged 4 – 17 years was measured whilst they read from a book, laptop, and desktop computer at a standard school chair and desk. Video images were captured and then digitized to calculate mean angles for head tilt, neck flexion, trunk flexion, and gaze angle. Posture was found to be influenced by IT type (p < 0.001), age (p < 0.001) and gender (p = 0.024) and significantly correlated to the stature of the participants. Measurement of resting posture and the maximal range of motion of the upper and lower cervical spines in the sagittal plane was also undertaken. The biophysical impact and the suitability of the three different information technologies are discussed.

Trend-resistant and cost-efficient cross-over designs for mixed models

A mixed model approach is used to construct optimal cross-over designs. In a cross-over experiment the same subject is tested at different points in time. Consider as an example an experiment to investigate the influence of physical attributes of the work environment such as luminance, ambient temperature and relative humidity on human performance of acceptance inspection in quality assurance. In a mixed model context, the subject effects are assumed to be independent and normally distributed. Besides the induction of correlated observations within the same inspector, the mixed model approach also enables one to specify the covariance structure of the inspection data. Here, several covariance structures are considered either depending on the time variable or not. Unfortunately, a serious drawback of the inspection experiment is that the results may be influenced by an unknown time trend because of inspector fatigue due to monotony of the inspection task. In other circumstances, time trend effects can be caused by learning effects of the test subjects in behavioural and life sciences, heating or ageing of material in prototype experiments, etc. In addition, the costs for using the subjects and for altering the factor levels between consecutive observations are also taken into account. An algorithm is presented to construct cost-efficient cross-over designs that are optimally balanced for time trend effects. The robustness of the computed run orders against misspecification of the covariance pattern is also investigated and a number of examples illustrate utility of the outlined design methodology.

The effects of imagery perspective as a function of skill level on alpha activity

A strategy being used by athletes to enhance their performance is imagery. In previous research studying imagery, Lang's (1977, 1979) Information-Processing Theory states two types of propositions: stimulus propositions (SP) and response propositions (RP). The beneficial use of imagery scripts emphasizing these propositions may depend on the skill level of the performer. The purpose of this study was to investigate differences in lower (8–10 Hz) and upper (11–13 Hz) alpha activities during imagery emphasizing SP and imagery emphasizing RP as related to the skill level of the subjects. Twenty-two right-handed male subjects were assigned to either an ‘expert’ ( n=11) or a ‘novice’ ( n=11) group. Lower and upper alpha activities from six active sites were recorded during imagery of a golf-putting task. After subsequent fast Fourier transform (FFT) analysis of results, mean lower and upper alpha power values were entered into separate repeated measures mixed model designs. Results revealed significant differences in skill level at the occipital sites in the lower alpha band. Moreover, a significant interaction between imagery perspective and skill level was found in the lower alpha band at the occipital site and in the upper alpha band at the parietal site. Significant differences were found in imagery perspective at the parietal, temporal, and occipital sites in the lower alpha band. In addition, a significant interaction effect, imagery perspective by hemisphere, was found in the upper alpha band at the parietal site. Conclusions are discussed based on the results and future research is suggested.

Cognitive processing of pain‐related words and psychological adjustment in high and low pain frequency participants

Objectives. This study tested the hypotheses that a group of students reporting a high number of pain episodes would present evidence of memory and processing time biases for pain‐related words and that they would be impaired on measures of mood when compared to a low pain frequency group. Design. A quasi‐experimental mixed model design was employed. Group (high pain frequency group, low pain frequency group) was the between‐participants factor, Wordtype (pain‐sensory, pain‐affective, neutral) and encoding condition (self, other‐reference) were the repeated measures. Percentage recall and processing time for each word type were used as dependent measures. Between‐groups comparisons were made for the questionnaire measures. Methods. A computerized word task comprising of pain‐sensory, pain‐affective and neutral words was administered to students. Students were asked to encode the words in a self‐ and other person reference condition followed by a delayed recall phase and the administration of the questionnaires. Results. The recall scores analysis showed that the high pain frequency students recalled significantly more affective words encoded in self‐reference than in the other‐reference. They also recalled significantly more sensory words encoded in self‐reference when compared to the low pain frequency group. The results of the processing time data showed that self‐reference encoding required significantly longer processing time. However, the high pain frequency group processed sensory words encoded in self‐reference significantly faster than neutral or affective words. There were no betweengroups differences on measurements of depression and anxiety. Conclusions. The results suggest that although mood levels are normal for a nonclinical young population experiencing a high number of pain episodes, they show some evidence of pain‐specific cognitive biases previously found in chronic pain patients. Future longitudinal research should assess whether these pain‐specific cognitive biases could be indicators of vulnerability to develop chronic pain in the future.

Balance and orthogonality in designs for mixed classification models

A classification model is easiest to analyze when it has a balanced design. Many of the nice features of balanced designs are retained by error-orthogonal designs, which were introduced in a recent paper by the authors. The present paper defines a kind of ‘‘partially balanced’’ design and shows that this partial balance is sufficient to ensure the error-orthogonality of a mixed classification model. Results are provided that make the partial balance condition easy to check. It is shown that, for a maximal-rank error-orthogonal design, the Type I sum of squares for a random effect coincides with the Type II sum of squares.

Mixed Methodology: Combining Qualitative and Quantitative Approaches

PART ONE: PARADIGMS AND POLITICS OF RESEARCH Introduction to Mixed Methods and Mixed Model Studies in the Social and Behavioral Sciences Pragmatism and the Choice of Research Strategy Research Design Issues for Mixed Method and Mixed Model Studies PART TWO: METHODS AND STRATEGIES OF RESEARCH Sampling, Measurement, and Quality of Inferences Data Collection Strategies and Research Procedures Alternatives to Traditional Data Analytic Strategies PART THREE: APPLICATIONS, EXAMPLES AND FUTURE DIRECTION OF MIXED MODEL RESEARCH Examples of Mixed Model Designs Extended Examples of Mixed Model Designs Conclusions and Future Directions

Young Students At Risk for Antisocial Behavior: The Utility of Academic and Social Skills Interventions

The effectiveness of academic and social skills interventions were compared using first-grade students identified by their classroom teachers as at risk for behavior problems. The aim of this study was to determine whether an academic or a social skills intervention would be more effective in increasing academic performance and social competence and in decreasing problem behavior. Academic, social, and behavioral outcome measures were examined using a mixed model design. None of the interaction terms was significant for any four dependent variables assessed. Findings pertaining to maintenance of effects indicated that, although improvements were not statistically significant, the improvements that did take place were maintained.Treatment acceptability ratings completed by student participants from each of the three intervention groups were favorable. Similarly, the majority of the teachers rated the interventions as highly acceptable. Logistical constraints of this study are examined, and direction for future research is provided.

Design of cross-over trials for pharmacokinetic studies

We describe a method for constructing D-optimal designs for nonlinear mixed effect models in cross-over pharmacokinetic studies. The method is based on fitting an approximate model using generalised least squares. The design construction is illustrated using an example motivated by a real clinical trial. The example shows that without period effects in the model, the optimal AB/BA design for estimating the treatment difference is independent of subject effects. When period effects are included the optimal design criterion changes significantly with the size of the between-subject variance but the consequences for the choice of optimal sampling times is small. The numerical results are discussed by exploring further the nature of the information matrix under certain conditions. Our results suggest that, under appropriate conditions, some optimality results that apply for linear model repeated measurement designs may also hold in the context of nonlinear mixed effect models.

A TEST OF THE GENERALITY OF THE EFFECTS OF SHELTER BOTTLENECKS IN FOUR STONE CRAB POPULATIONS

The structural complexity of a habitat dictates the availability of shelter, and shelter may affect population and community structure in many systems. I tested predictions from the shelter bottleneck hypothesis, which proposes that shelter (or refuge) limitation can control population size structure and density by acting strongly on only one size class. I manipulated shelter for stone crabs in four haphazardly chosen bays in the northeast Gulf of Mexico to examine the shelter bottleneck hypothesis in a mixed-model design. I also examined four biotic factors (habitat structure, food, predation, and interspecific competition) that may contribute to population-level differences among bays. I found differences among bays in stone crab size structure and density and in crab responses to size-specific shelter supplementation. These differences in stone crabs among bays included: (1) natural median crab size differed by 5.5-fold, (2) size at maturity changed by 33%, (3) adult density varied 10-fold, (4) the den...

Stuck in the Model Trap: The Effects of Beautiful Models in Ads on Female Pre-Adolescents and Adolescents

One of advertising's “unintended effects” is the impact highly attractive models may have on female pre-adolescents and adolescents. Using social comparison theory as a framework, the authors propose that young girls compare their physical attractiveness with that of advertising models and, subsequently, their self-perceptions and self-esteem may be affected, depending on the motive for social comparison. They report a study with a mixed-model design in which motive was manipulated. Girls in grades four, six, and eight participated. The results suggest that motive is important, as support was found for all hypotheses. However, the support was not consistent across all grades or for all dependent variables. The authors consider possible reasons for the inconsistency and discuss the implications of the findings for advertisers and educators.

Inference and Generality in Ecology: Current Problems and an Experimental Solution

Two major points are considered: I) the growth of ecology is constrained and the scientific credibility of ecologists is reduced, because too many generalizations are accepted on insufficient evidence, and 2) there are experimental methods for addressing this problem. I illustrate problems that arise from theories that, although valid in limited domains, have been excessively generalized, and I examine methods for decreasing the disparity in populations considered between statistical inferences and scientific generalizations. The use of random factors in experimental designs helps to address the domain in which generalizations are valid, because the statistical population encompassed by random factors is much larger than that addressed typically by fixed factors. The use of random factors is considered in particular in mixed-model ANOVAs, because the basic techniques are well described and familiar to most ecologists. Mixed-model designs provide a strong experimental framework and address many of the problems with other methods for assessing the generality of ecological theories. No single experimental design will be sufficient to define the broader generalities that ecologists seek, but these designs should be included more often in research programs.

Enhancing Comprehension and Retention of Safety-Related Pictorials

Because of their relatively universal information transmission potential, pictorials have been suggested as a common means of safety communications across heterogeneous groups of users and uses. The present study used a training paradigm designed to enhance comprehension and retention of pharmaceutical and industrial-safety pictorials. Manipulated were time of testing (prior to training, immediately following training, and after a one-week delay), content of instruction (supplying the associated verbal label vs. the verbal label plus an extra explanatory statement), and difficulty level (“easy” vs. “difficult” to understand pictorials according to comprehension rates in earlier studies). Using an incomplete factorial mixed-model design experiment, the results showed substantial training effects. There was little change in scores between the test immediately after training and the test after a one-week delay (and the final test scores did not differ between participants who took or did not take the immediate post-training test). Easy pictorials were comprehended (both initially and following training) better than difficult pictorials, although the latter showed the most dramatic increase in understandability after training. Additionally, the instruction content manipulation (adding the explanatory statement to the verbal label)—which had been expected to influence the degree of encoding–had no effect on retention. The substantial gains in understanding the more difficult pictorials suggest that brief training, as little as giving the pictorial's verbal meaning once, can have a large impact in facilitating comprehension for pictorials that would otherwise not be understood by many people.

Contrasting cognitive deficits in attention deficit hyperactivity disorder versus reading disability.

We compared 2 common and sometimes comorbid developmental disorders, reading disability (RD) and attention deficit hyperactivity disorder (ADHD), in 2 cognitive domains, phonological processes (PP) and executive functions (EF). Subjects were 70 boys of early school age, studied by means of a 2 (RD vs. no RD) × 2 (ADHD vs. no ADHD) × 2 (domain type) mixed-model design. The 2 RD groups (RD-only and RD plus ADHD) were significantly impaired compared with both the control and ADHD-only groups on a PP composite score but performed normally on the EF composite score. The ADHD-only group had an opposite profile and was significantly different from both RD groups and from controls on the EF composite score. Thus, there was a double-dissociation between the RD-only and ADHD-only groups. The comorbid group resembled the RDonly group, consisttent with the hypothesis that their ADHD symptoms are secondary to RD

THE EFFECT OF LEARNING ON THE OPERATION OF MIXED‐MODEL ASSEMBLY LINES

The common approach to balancing mixed‐model assembly lines assumes that the line operators are well trained and that the learning effect is negligible. The assumption is that the line operates in steady state over a long period of time. Time‐based competition and frequent design changes in many products make this assumption incorrect, and the effect of learning on mixed‐model lines should not be neglected.We defined start‐up period and developed a model for the line design during start‐up. It can be used to evaluate a proposed line design or to develop a feasible line design and to estimate its cost. This proposed model integrates mixed‐model learning curves with aggregate planning under learning and a mixed‐model line design into a comprehensive framework designed to minimize the total cost of the line during the start‐up period.

Frequency, duration, and speed of wheel running of rats as a function of age and starvation

The purpose of this experiment was to determine whether age differences in amounts of wheel running of starved rats were due to the frequency of bursts of running, to the average duration of bursts, to speed, or to any combination of these parameters. The experiment was carried out according to a 3 by 2 by 2 mixed model design. The independent variables were age (67, 293, and 746 days old at the start of starvation), food deprivation (total starvation vs ad lib), and occasion of measurement (initial vs maximum activity). The dependent variables were number of wheel revolutions, number of bursts of activity, number of seconds of running per burst, and revolutions per second. The results indicated that acutely starved rats run more often, for longer periods, and at higher speeds than do sated rats, and that with increased age rats run less often, for a shorter time, and at slower speeds.

Comment on “The Trouble with Concept Testing”

This comment concerns an inappropriate use of the analysis of variance (ANOVA) by Haley and Gatty in their recent study Trouble With Concept Testing [1]. Haley and Gatty studied the difference between abstract product and their execution by measuring consumer reactions to 24 copy executions (8 different concepts executed by 3 different Copywriters). Haley and Gatty used a 2 variable (Concept and Copywriters) fixed constants ANOVA based on one measurement per respondent. This ANOVA model is not correct for their experimental design, where each respondent was measured 24 times, once for each of the 24 copy executions. Accordingly, the means for each of the 24 copy executions are correlated, since each respondent contributed a score to each copy execution mean. Comparison of the 24 copy execution means requires an ANOVA model which accounts for the correlated measurements. The appropriate ANOVA for the Haley and Gatty data is a mixed model design, where Concepts and Copywriters are treated as fixed constants and Respondents is a variable based on random sampling, see McNemar [2]. This mixed model ANOVA determines the mean sauare for 7 sources defined by the experimental design, i.e.:

The Analysis of Repeated Measures and other Mixed-Model ANOVA Designs

The Analysis of Repeated Measures and other Mixed-Model ANOVA Designs

Minimal Sufficient Statistics for the Two-Way Classification Mixed Model Design

Minimal Sufficient Statistics for the Two-Way Classification Mixed Model Design