Multilevel Models for the Analysis of Angle-Specific Torque Curves with Application to Master Athletes

Application of Hierarchical/Multilevel Models and Quality of Reporting (2010-2020): A Systematic Review

Introduction

Multilevel models have gained immense popularity across almost every discipline due to the presence of hierarchy in most data and phenomena. In this paper, we present a systematic review on the adoption and application of multilevel models and the important information reported on the results generated from the use of these models.

Methods

The review was performed by searching Google Scholar for original research articles on the application of multilevel models published between 2010 and 2020. The search strategy involved topics such as "multilevel models," "hierarchical linear models," and "mixed models with hierarchy." The search placed more emphasis on the application of hierarchical models in any discipline but excluded software methodological development and related articles.

Results

A total of 121 articles were initially obtained from the search results. However, 65 articles met the inclusion criteria for the review. Out of the 65 articles reviewed, 46.2% were related to health/epidemiology, 15.4% to education and psychology, and 16.9% to social life. The majority of the articles (78.5%) were two-level models, and most of these studies modelled univariate responses. However, the few that modelled more than one response modelled them separately. Moreover, 83.1% were cross-sectional design, and 9.2% and 6.2% were longitudinal and repeated measures, respectively. Moreover, a little over half (55.4%) of articles reported on the intraclass correlation measure, and all articles indicated the response variable distribution where most (47.7%) were normally distributed. Only 58.5% of articles reported on the estimation methods used as Bayesian (20%) and MLE (18.5%). Again, model validation measures and statistical software were reported in 70.8% and 90.8% articles, respectively.

Conclusion

There is an increase in the utilization of multilevel modelling in the last decade, which could be attributed to the presence of clustered and hierarchically correlated data structures. There is a need for improvement in the area of measurement and reporting on the intraclass correlation, parameter estimation, and variable selection measures to further improve the quality of the application of multilevel models. The integration of spatial effects into multilevel models is very limited and needs to be explored in the future.

Modeling the Angle-Specific Isokinetic Hamstring to Quadriceps Ratio Using Multilevel Generalized Additive Models

Background and Objectives: This study considered the use of a generalized additive multilevel model to describe the joint-angle-specific functional hamstring to quadriceps ratio (H:Q ratio) in the knee, using all of the available truly isokinetic data within the range. Materials and Methods: Thirty healthy male basketball players aged 15.0 (1.4) years (average stature = 180.0 cm, SD = 11.1 cm; average body mass = 71.2, SD = 14.9 kg) years were considered. All players considered had no history of lower extremity musculoskeletal injury at the time of testing or during the 6 months before testing, and had been engaged in formal basketball training and competition for 5.9 (2.4) years. Moments of force of the reciprocal concentric and eccentric muscular actions for the knee extensors and flexors assessed by isokinetic dynamometry at 60°∙s⁻¹ were used. Results: Maximum moments of force were attained at different angle positions for knee extension. For knee flexion, it was apparent that there was an ability to maintain high levels of moment of force between 30° and 60° in the concentric muscular action, corresponding to the concentric action of the hamstrings. However, for the eccentric knee flexion, corresponding to the quadriceps action, there was a marked peak of moment of force at about 55°. The functional H:Q ratio for the knee extension was non-linear, remaining higher than 1.0 (i.e., point of equality) from the beginning of the extension until approximately 40° of the knee extension, leveling off below the point of equality thereafter. On average, the functional H:Q ratio for the knee flexion did not attain 1.0 across the range of motion. The functional H:Q ratio for the knee in the present sample peaked at 20° and 80°, declining between these angle positions to below 0.50 at about 0.54. Conclusions: Estimating the form of the non-linear relationship on-the-fly using a generalized additive multilevel model provides joint-angle-specific curves and joint-angle-specific functional H:Q ratio patterns, allowing the identification and monitoring of strength development, with potential implications for injury and performance.

Feasibility of the two-point method for assessing the force-velocity relationship during lower-body and upper-body isokinetic tests

This study aimed to (1) evaluate the shape of the force-velocity (F-V) relationship obtained from different muscles, (2) explore the concurrent validity of the two-point method with respect to the multiple-point method, (3) evaluate whether the F-V relationship can discriminate between muscle groups and genders, and (4) explore the generalisability of the same F-V relationship parameters (maximal force [F₀], maximal velocity [V₀]), and maximal power [P₀]) between different tasks. The F-V relationship of 22 physically active participants (12 women) were tested during knee extension, knee flexion, elbow extension and elbow flexion through the multiple- (eight velocities: 30-60-90-120-150-180-210-240º/s) and two-point (two velocities: 60-180º/s) methods. The findings revealed (1) highly linear F-V relationships (r ≥ 0.893), (2) high concurrent validity of the two-point method for F₀, but lower for V₀ and P₀, (3) the outcomes of both methods were sensitive to the muscle groups (higher for knee muscles) and gender (higher for men), and (4) the magnitude of the same F-V parameters were poorly correlated between different tasks (median r < 0.1). These results support the two-point method as a valid and sensitive procedure for determining the maximal capacities of the muscles to produce F, but not V, during isokinetic tests.