Postural Stability, Rather than Strength–Coordination, Is Associated with Executive Functions in Preschool Children: A Structural Equation Modeling Study

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

I would like to thank for the opportunity to review this manuscript. Please see the following comments to consider to further increase the quality of this manuscript.

The manuscript addresses an important and timely topic by examining the relationships between executive functions, motor performance, physical activity, and waist circumference in preschool children using structural equation modeling. The study is based on a relatively large sample of preschool-aged children and attempts to move beyond global motor competence scores by distinguishing between postural stability and strength-coordination domains. This distinction represents a potentially meaningful contribution to the literature, particularly given the increasing interest in identifying specific motor processes that may be associated with executive functioning during early childhood. The use of SEM is also a strength because it allows the simultaneous examination of direct and indirect pathways while accounting for measurement error. Overall, the manuscript is clearly structured, theoretically grounded, and addresses a research question of practical relevance for developmental, educational, and pediatric research.

The introduction provides a coherent rationale for the study and successfully identifies a gap in the literature regarding the differential roles of motor domains in executive functioning. The hypotheses are clearly stated and logically derived from previous research. However, the theoretical justification for distinguishing postural stability from strength-coordination could be developed further. While the authors argue that balance tasks involve greater demands on sensory integration and self-regulation, this argument would benefit from a deeper integration of neurodevelopmental and embodied cognition perspectives. Perhaps the authors could elaborate more extensively on the shared neural substrates underlying postural control and executive functioning, particularly the involvement of cerebellar and prefrontal networks. Such an expansion would strengthen the theoretical foundation of the study and provide a clearer explanation for the observed associations.

The methodology is generally well described, but several aspects require clarification and further justification. The use of a convenience sample limits the representativeness of the findings, and this issue deserves greater consideration in both the Methods and Discussion sections. In addition, the age range of 4–7 years encompasses substantial developmental variability in both motor and executive functions. Although age was statistically controlled, perhaps the authors should consider whether developmental differences across this age span may influence the observed relationships. Exploratory analyses by narrower age groups or age moderation analyses could provide valuable additional insights.

The measurement of executive functions represents one of the main limitations of the study. The CHEXI is a valid and useful ecological measure; however, it captures parent perceptions of executive functioning rather than objective executive performance. Consequently, the findings should be interpreted as associations between motor performance and parent-reported executive difficulties rather than executive functions per se. The manuscript would benefit from a more explicit discussion of this distinction. Future studies should ideally combine questionnaire-based assessments with performance-based executive function tasks to provide a more comprehensive evaluation of the construct.

The motor assessment procedures are generally appropriate, but there appears to be some inconsistency regarding the composition of the strength-coordination construct. Table 1 includes tiptoe walking and hopping measures, yet these variables do not appear to be incorporated into the final latent model. The authors should clearly explain why these variables were excluded and whether alternative measurement models including these indicators were evaluated. Greater transparency regarding model development would improve confidence in the final specification.

The SEM approach is appropriate; however, several methodological concerns require attention. First, the use of two-indicator latent variables for Executive Functions and Postural Stability remains problematic despite the authors' justification. Although such models can be identified, they are generally less stable and provide limited opportunities for evaluating construct validity. The manuscript acknowledges this limitation, but perhaps the authors should provide additional evidence regarding the reliability of these latent factors, such as composite reliability or average variance extracted estimates.

Second, the decision to remove several theoretically relevant variables from the final model raises concerns about potential model overfitting. Screen time, sleep duration, healthy eating score, and BMI were initially included but subsequently excluded because they were not statistically significant. While model parsimony is important, removing variables solely on statistical grounds may introduce a degree of data-driven model modification. It would strengthen the manuscript if the authors reported the full initial model and provided a more detailed comparison between the initial and final specifications, including fit indices and parameter estimates.

Third, the handling of missing data warrants reconsideration. Median imputation is generally not recommended in SEM because it can distort variances, covariances, and standard errors. Given that SEM software commonly supports Full Information Maximum Likelihood estimation, perhaps the authors should consider reanalyzing the data using FIML. Even though the proportion of missing data was relatively small, employing a more rigorous approach would improve methodological robustness.

Several statistical reporting issues should also be addressed. In Table 2, some p-values appear inconsistent with the reported z-values. For example, an inhibition loading with a z-value of 4.655 is associated with a p-value of 0.227, which appears implausible. Similar inconsistencies are present for several other indicators. In Table 3, the age effect on postural stability is reported as β = 0.37 with z = 7.826 but p = 0.107, which is statistically impossible. Likewise, the age effect on strength-coordination reports z = 5.64 and p = 1.692. These apparent errors raise concerns regarding the accuracy of the reported output and should be carefully reviewed before publication. The authors should verify all tables and ensure consistency between parameter estimates, standard errors, z-values, and p-values.

The results are generally presented clearly, and the distinction between postural stability and strength-coordination is interesting. Nevertheless, the practical significance of the findings deserves greater discussion. The model explained only 9.6% of the variance in executive functions, suggesting that the observed relationships, although statistically significant, account for a relatively small proportion of executive-function variability. The Discussion should place greater emphasis on effect sizes and practical implications rather than focusing primarily on statistical significance.

The interpretation of the indirect effects should also be somewhat more cautious. The significant indirect effect involving waist circumference was relatively small, and the confidence interval approached zero. Furthermore, because the study is cross-sectional, mediation terminology should be used carefully. Although the authors appropriately acknowledge the inability to infer causality, terms such as “mediated pathway” may still imply causal mechanisms that cannot be established from cross-sectional data. Perhaps the authors should consistently refer to these findings as indirect statistical associations rather than mediation effects.

The Discussion is generally balanced and appropriately integrates the findings with previous literature. However, it would benefit from a more critical consideration of alternative explanations. For example, unmeasured factors such as socioeconomic status, parental education, general developmental maturity, or participation in organized physical activities could potentially influence both motor performance and executive functioning. A more comprehensive discussion of possible confounding variables would strengthen the interpretation of the findings.

The Conclusions are generally supported by the results, although some statements may be slightly stronger than warranted given the cross-sectional design and modest explained variance. The authors may wish to emphasize that postural stability was associated with executive functioning rather than implying a particularly influential developmental role. Such wording would better reflect the observational nature of the study.

In summary, this manuscript addresses an important topic and has several strengths, including its sample size, theoretical focus on specific motor domains, and use of structural equation modeling. However, before publication, the manuscript would benefit from substantial revisions addressing concerns related to measurement validity, model specification, missing data treatment, statistical reporting accuracy, and interpretation of indirect effects. Particular attention should be given to the apparent inconsistencies in Tables 2 and 3, as these issues raise questions regarding the reliability of the reported analyses. With these revisions, the manuscript could make a meaningful contribution to understanding the relationship between motor performance and executive functioning during early childhood.

Author Response

REVIEWER 1

Would like to thank for the opportunity to review this manuscript. Please see the following comments to consider to further increase the quality of this manuscript.

• The manuscript addresses an important and timely topic by examining the relationships between executive functions, motor performance, physical activity, and waist circumference in preschool children using structural equation modeling. The study is based on a relatively large sample of preschool-aged children and attempts to move beyond global motor competence scores by distinguishing between postural stability and strength-coordination domains. This distinction represents a potentially meaningful contribution to the literature, particularly given the increasing interest in identifying specific motor processes that may be associated with executive functioning during early childhood. The use of SEM is also a strength because it allows the simultaneous examination of direct and indirect pathways while accounting for measurement error. Overall, the manuscript is clearly structured, theoretically grounded, and addresses a research question of practical relevance for developmental, educational, and pediatric research.

A: We sincerely thank the reviewer for this positive and encouraging assessment of our work. We appreciate the recognition of the study's theoretical rationale, the distinction between postural stability and strength-coordination domains, the relatively large sample size, and the use of structural equation modeling to examine the relationships among executive functions, motor performance, physical activity, and waist circumference in preschool children. We are pleased that the reviewer considers the research question relevant for developmental, educational, and pediatric research. No modifications to the manuscript were required in response to this comment.

• The introduction provides a coherent rationale for the study and successfully identifies a gap in the literature regarding the differential roles of motor domains in executive functioning. The hypotheses are clearly stated and logically derived from previous research. However, the theoretical justification for distinguishing postural stability from strength-coordination could be developed further. While the authors argue that balance tasks involve greater demands on sensory integration and self-regulation, this argument would benefit from a deeper integration of neurodevelopmental and embodied cognition perspectives. Perhaps the authors could elaborate more extensively on the shared neural substrates underlying postural control and executive functioning, particularly the involvement of cerebellar and prefrontal networks. Such an expansion would strengthen the theoretical foundation of the study and provide a clearer explanation for the observed associations.

A: We thank the reviewer for this valuable suggestion. We agree that a more detailed neurodevelopmental rationale can strengthen the theoretical foundation for distinguishing postural stability from broader strength-coordination performance. Accordingly, we have expanded the Introduction by incorporating additional discussion of the shared neural substrates underlying postural control and executive functioning, including the potential roles of cerebellar–prefrontal networks. We also incorporated an embodied cognition perspective to provide a broader developmental framework for understanding why balance-related processes may be particularly relevant to executive functioning during early childhood. These additions have been incorporated into the Introduction.

• The methodology is generally well described, but several aspects require clarification and further justification. The use of a convenience sample limits the representativeness of the findings, and this issue deserves greater consideration in both the Methods and Discussion sections. In addition, the age range of 4–7 years encompasses substantial developmental variability in both motor and executive functions. Although age was statistically controlled, perhaps the authors should consider whether developmental differences across this age span may influence the observed relationships. Exploratory analyses by narrower age groups or age moderation analyses could provide valuable additional insights.

A: We thank the reviewer for this thoughtful observation. We agree that the use of a convenience sample limits the generalizability of the findings. To address this concern, we have strengthened the discussion of sampling limitations in both the Methods and Discussion sections, explicitly acknowledging that the sample may not be fully representative of the broader preschool population.

Regarding age, we agree that the 4–7-year age range encompasses substantial developmental changes in both motor and executive functions. In the present study, age was included as a covariate in all structural models to account for developmental variability. However, the primary objective was to examine the overall pattern of associations among executive functions, motor performance, physical activity, and waist circumference rather than to investigate age-specific effects. We have now expanded the Limitations section to acknowledge that future studies should examine whether these associations differ across narrower developmental stages or are moderated by age.

• The measurement of executive functions represents one of the main limitations of the study. The CHEXI is a valid and useful ecological measure; however, it captures parent perceptions of executive functioning rather than objective executive performance. Consequently, the findings should be interpreted as associations between motor performance and parent-reported executive difficulties rather than executive functions per se. The manuscript would benefit from a more explicit discussion of this distinction. Future studies should ideally combine questionnaire-based assessments with performance-based executive function tasks to provide a more comprehensive evaluation of the construct.

A: We thank the reviewer for this important observation. We agree that the CHEXI captures parent-reported manifestations of executive functioning in everyday contexts rather than objective executive performance assessed through neuropsychological tasks. Although the CHEXI has demonstrated adequate psychometric properties and ecological validity in preschool populations, we acknowledge that it reflects caregiver perceptions of executive difficulties. To address this concern, we have expanded the Discussion and Limitations sections to explicitly clarify this distinction and to emphasize that the observed associations should be interpreted in relation to parent-reported executive-function difficulties rather than objective executive performance. We have also added a statement highlighting the value of combining questionnaire-based and performance-based measures of executive functioning in future studies.

• The motor assessment procedures are generally appropriate, but there appears to be some inconsistency regarding the composition of the strength-coordination construct. Table 1 includes tiptoe walking and hopping measures, yet these variables do not appear to be incorporated into the final latent model. The authors should clearly explain why these variables were excluded and whether alternative measurement models including these indicators were evaluated. Greater transparency regarding model development would improve confidence in the final specification.

A: We thank the reviewer for this important observation. We agree that greater transparency regarding model development is warranted. Tiptoe walking and hopping were initially considered as potential indicators during the development of the measurement model. Alternative measurement models including these indicators were explored; however, tiptoe walking and hopping showed comparatively weak contributions to the latent structure and were associated with less satisfactory overall model fit. Consequently, these indicators were removed during the model refinement process in order to achieve a more parsimonious and theoretically coherent measurement model. To clarify this issue, we have added a description of the model development process in the Statistical Analysis section and explicitly stated the rationale for excluding these indicators from the final SEM specification.

• The SEM approach is appropriate; however, several methodological concerns require attention. First, the use of two-indicator latent variables for Executive Functions and Postural Stability remains problematic despite the authors' justification. Although such models can be identified, they are generally less stable and provide limited opportunities for evaluating construct validity. The manuscript acknowledges this limitation, but perhaps the authors should provide additional evidence regarding the reliability of these latent factors, such as composite reliability or average variance extracted estimates.

A: We thank the reviewer for this valuable methodological observation. We agree that latent variables defined by only two indicators provide more limited opportunities for evaluating construct validity than factors represented by three or more indicators. We explored the possibility of calculating Composite Reliability (CR) and Average Variance Extracted (AVE); however, the standardized measurement solution required for valid estimation of these indices was not available from the final SEM output. Rather than reporting potentially unreliable values derived from identification-constrained loadings, we opted for a more conservative approach.

As supplementary evidence of indicator consistency, we examined the correlations between the paired indicators defining each latent construct. Working memory and inhibition showed a strong positive correlation (r = 0.698, p < 0.001), while right- and left-leg balance showed a moderate-to-strong positive correlation (r = 0.547, p < 0.001). These results have been added to the Supplementary Materials (Table S1) and are now briefly described in the Results section. We also expanded the discussion of this limitation and continue to acknowledge that future studies should incorporate a broader set of indicators for both executive functioning and postural stability.

• Second, the decision to remove several theoretically relevant variables from the final model raises concerns about potential model overfitting. Screen time, sleep duration, healthy eating score, and BMI were initially included but subsequently excluded because they were not statistically significant. While model parsimony is important, removing variables solely on statistical grounds may introduce a degree of data-driven model modification. It would strengthen the manuscript if the authors reported the full initial model and provided a more detailed comparison between the initial and final specifications, including fit indices and parameter estimates.

A: We thank the reviewer for this thoughtful observation. We agree that removing variables solely on statistical grounds may increase the risk of data-driven model modification and potentially raise concerns regarding model overfitting. We would like to clarify, however, that the reported SEM was not derived through a formal sequential elimination procedure applied to a fully estimated initial model. Rather, several lifestyle and anthropometric variables were considered during the conceptual development phase based on their theoretical relevance and previously reported associations with cognitive and motor development.

The final SEM specification was determined using a theory-informed and parsimonious approach that prioritized variables most closely aligned with the study aims and conceptual framework. Physical activity and waist circumference were retained because they were central to the study hypotheses, while age and sex were retained as a priori covariates due to their established developmental relevance. Screen time, sleep duration, healthy eating score, and body mass index were explored during model development but were not retained in the final specification because they were not central to the primary research questions and did not meaningfully improve model interpretation.

To avoid the impression that the final model resulted from a purely data-driven variable selection process, we have revised the Model Specification section to clarify the rationale underlying model development and variable selection. We have also emphasized that the final SEM should be interpreted as a theoretically grounded and parsimonious representation of the relationships most relevant to the study aims rather than as the result of iterative statistical optimization.

• Third, the handling of missing data warrants reconsideration. Median imputation is generally not recommended in SEM because it can distort variances, covariances, and standard errors. Given that SEM software commonly supports Full Information Maximum Likelihood estimation, perhaps the authors should consider reanalyzing the data using FIML. Even though the proportion of missing data was relatively small, employing a more rigorous approach would improve methodological robustness.

A: We thank the reviewer for this valuable suggestion. We agree that Full Information Maximum Likelihood (FIML) is generally considered a more rigorous approach for handling missing data in SEM than simple imputation methods. In response to the reviewer's recommendation, we re-estimated the final SEM using FIML and compared the resulting parameter estimates with those obtained from the original median-imputation approach.

The key structural coefficients were highly consistent across both approaches. Importantly, the central findings of the study remained unchanged. Physical activity and waist circumference continued to show significant associations with Postural Stability, Postural Stability remained significantly associated with Executive Functions, and Strength-Coordination remained unrelated to Executive Functions. The magnitude of these effects was also highly similar across estimation methods. Although a small number of secondary covariate effects showed minor differences, the overall pattern of results and substantive interpretation of the model remained unchanged.

To document this robustness analysis, we have added a sensitivity analysis to the Results section and included a supplementary table (Supplementary Table S6) comparing the original model with the FIML re-estimated model. These additional analyses indicate that the main conclusions of the study are robust to the alternative missing-data handling approach.

We nevertheless acknowledge that future SEM studies should preferentially employ FIML or multiple-imputation approaches as the primary strategy for handling missing data whenever feasible.

• Several statistical reporting issues should also be addressed. In Table 2, some p-values appear inconsistent with the reported z-values. For example, an inhibition loading with a z-value of 4.655 is associated with a p-value of 0.227, which appears implausible. Similar inconsistencies are present for several other indicators. In Table 3, the age effect on postural stability is reported as β = 0.37 with z = 7.826 but p = 0.107, which is statistically impossible. Likewise, the age effect on strength-coordination reports z = 5.64 and p = 1.692. These apparent errors raise concerns regarding the accuracy of the reported output and should be carefully reviewed before publication. The authors should verify all tables and ensure consistency between parameter estimates, standard errors, z-values, and p-values.

A: We sincerely thank the reviewer for carefully identifying these inconsistencies. Following this observation, we conducted a comprehensive audit of all SEM-related tables and cross-checked every reported parameter against the original model output.

This review confirmed that the parameter estimates, standard errors, and z-values reported in the manuscript were correct. However, several p-values were inadvertently misreported during the preparation and formatting of the tables. Specifically, some parameters associated with extremely small p-values were originally exported in scientific notation, and formatting/transcription errors during table preparation resulted in incorrect values being displayed in the manuscript tables.

All affected tables have now been corrected and verified against the original SEM output. Table 2 was revised to ensure that all reported factor loadings and associated statistics correspond exclusively to the final measurement model, and the p-values were corrected accordingly. Table 3 was similarly reviewed and corrected, including parameters for which scientific notation had been improperly converted during formatting. In addition, all supplementary SEM tables were rechecked to ensure complete consistency throughout the manuscript.

Importantly, these corrections affect only the presentation of the statistical results and do not alter the parameter estimates, statistical significance of the reported effects, interpretation of the findings, overall pattern of results, or conclusions of the study.

We are grateful to the reviewer for bringing this issue to our attention, as it allowed us to improve the accuracy, transparency, and consistency of the statistical reporting throughout the manuscript.

• The results are generally presented clearly, and the distinction between postural stability and strength-coordination is interesting. Nevertheless, the practical significance of the findings deserves greater discussion. The model explained only 9.6% of the variance in executive functions, suggesting that the observed relationships, although statistically significant, account for a relatively small proportion of executive-function variability. The Discussion should place greater emphasis on effect sizes and practical implications rather than focusing primarily on statistical significance.

A: We thank the reviewer for this important observation. We agree that statistical significance should be interpreted alongside effect sizes and explained variance, particularly when examining complex developmental constructs such as executive functions.

In response to this comment, we expanded the Discussion to explicitly acknowledge that the model explained a relatively modest proportion of the variance in Executive Functions (R² = 9.6%). We now emphasize that the findings should not be interpreted as indicating that motor performance is a major determinant of executive functioning. Rather, the results suggest that Postural Stability represents one of several factors that may be associated with everyday executive functioning during early childhood, while recognizing that executive functions are influenced by numerous biological, environmental, educational, family, and behavioral factors that were not included in the present model.

We also revised the discussion of practical implications to place greater emphasis on the magnitude and interpretation of the observed effects rather than on statistical significance alone. Specifically, we highlight that the primary contribution of the study lies in identifying a specific motor domain, Postural Stability, that appears to be more closely related to executive functioning than broader Strength-Coordination performance.

Finally, the Conclusions section was revised to explicitly acknowledge the modest magnitude of the observed associations and to avoid overstating their practical significance. At the same time, we emphasize the potential value of Postural Stability as a promising domain for future longitudinal and experimental research examining the relationship between motor and executive-function development during early childhood.

• The interpretation of the indirect effects should also be somewhat more cautious. The significant indirect effect involving waist circumference was relatively small, and the confidence interval approached zero. Furthermore, because the study is cross-sectional, mediation terminology should be used carefully. Although the authors appropriately acknowledge the inability to infer causality, terms such as “mediated pathway” may still imply causal mechanisms that cannot be established from cross-sectional data. Perhaps the authors should consistently refer to these findings as indirect statistical associations rather than mediation effects.

A: We thank the reviewer for this thoughtful methodological observation. We agree that caution is warranted when interpreting indirect effects derived from cross-sectional SEM analyses and that terminology associated with mediation may inadvertently imply causal mechanisms that cannot be established from the present design.

In response to this comment, we carefully revised the manuscript to adopt more conservative and methodologically appropriate terminology throughout. References to “motor-mediated pathways” and related expressions were replaced with terms such as “indirect effects,” “indirect associations,” or “indirect statistical associations,” as appropriate. For example, in the Methods section, we now state that total, direct, and indirect effects were examined to distinguish between direct associations and indirect statistical associations involving the motor domain.

We also expanded the Discussion to explicitly acknowledge that the observed indirect effects represent statistical associations within a cross-sectional model and should not be interpreted as evidence of causal mediation. In addition, we now emphasize that the indirect association involving waist circumference was relatively small and that its confidence interval approached zero, warranting cautious interpretation. The revised text further notes that longitudinal and experimental studies are necessary to establish temporal ordering and determine whether these associations reflect causal developmental processes.

We believe these revisions provide a more balanced and appropriately cautious interpretation of the indirect effects while preserving the substantive contribution of the findings.

• The Discussion is generally balanced and appropriately integrates the findings with previous literature. However, it would benefit from a more critical consideration of alternative explanations. For example, unmeasured factors such as socioeconomic status, parental education, general developmental maturity, or participation in organized physical activities could potentially influence both motor performance and executive functioning. A more comprehensive discussion of possible confounding variables would strengthen the interpretation of the findings.

A: We thank the reviewer for this valuable suggestion. We agree that unmeasured factors may contribute to the observed associations and that consideration of alternative explanations strengthens the interpretation of the findings.

In response to this comment, we expanded the Limitations section to explicitly acknowledge the possibility of residual confounding. We now note that, although the analyses adjusted for age and sex, other potentially relevant factors—including socioeconomic status, parental education, participation in organized physical activities, characteristics of the home environment, and broader aspects of developmental maturity—were not available in the present dataset and may influence both motor performance and executive functioning during early childhood. We also supported this statement with references to previous literature highlighting the role of environmental, developmental, and socioeconomic factors in executive-function development.

Furthermore, we now emphasize that residual confounding cannot be ruled out and that the observed associations should therefore be interpreted within the context of these unmeasured influences. We believe this addition provides a more balanced discussion of alternative explanations and strengthens the interpretation of the study findings.

• The Conclusions are generally supported by the results, although some statements may be slightly stronger than warranted given the cross-sectional design and modest explained variance. The authors may wish to emphasize that postural stability was associated with executive functioning rather than implying a particularly influential developmental role. Such wording would better reflect the observational nature of the study.

A: We thank the reviewer for this thoughtful comment and agree that the Conclusions should remain closely aligned with the observational nature of the study and the modest proportion of variance explained in Executive Functions.

In response, we revised the Conclusions section to adopt more cautious wording. Specifically, we reduced language that could be interpreted as implying a particularly influential developmental role for postural stability and instead emphasized that postural stability was associated with executive functioning within the present sample. We also retained explicit acknowledgment that the observed associations were modest in magnitude and highlighted the need for longitudinal and experimental studies to clarify the nature and developmental significance of these relationships.

We believe these revisions provide a more balanced interpretation of the findings and better reflect the limitations inherent to the cross-sectional design.

• In summary, this manuscript addresses an important topic and has several strengths, including its sample size, theoretical focus on specific motor domains, and use of structural equation modeling. However, before publication, the manuscript would benefit from substantial revisions addressing concerns related to measurement validity, model specification, missing data treatment, statistical reporting accuracy, and interpretation of indirect effects. Particular attention should be given to the apparent inconsistencies in Tables 2 and 3, as these issues raise questions regarding the reliability of the reported analyses. With these revisions, the manuscript could make a meaningful contribution to understanding the relationship between motor performance and executive functioning during early childhood.

A: We sincerely thank the reviewer for the careful and constructive evaluation of our manuscript and for recognizing its strengths, including the sample size, the focus on specific motor domains, and the use of structural equation modeling.

In response to the reviewer's comments, we have substantially revised the manuscript. Specifically, we expanded the discussion of measurement validity, provided additional justification and transparency regarding model specification, conducted a sensitivity analysis using Full Information Maximum Likelihood (FIML) to evaluate the robustness of the findings to missing-data handling, corrected and verified all statistical tables against the original SEM output, and adopted more cautious language when interpreting indirect effects and cross-sectional associations.

Particular attention was devoted to the inconsistencies identified in Tables 2 and 3. Following a comprehensive audit of the SEM outputs, all reporting errors were corrected and all parameter estimates, standard errors, z-values, and p-values were verified against the original model results. Importantly, these corrections affected only the presentation of the results and did not alter the substantive findings or conclusions of the study.

We are grateful for the reviewer's thoughtful suggestions, which have substantially improved the clarity, transparency, and methodological rigor of the manuscript. We hope that the revised version adequately addresses all concerns and provides a stronger contribution to the literature on motor performance and executive functioning during early childhood.

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript addresses a relevant topic; however, substantial improvements are required before it can be considered for publication. The introduction does not provide sufficient background, and several key references in the field are missing. The rationale for the study is not clearly articulated, and the research questions are not well connected to the existing literature. The research design appears conceptually appropriate, but the methodological description lacks clarity and detail in several sections, making it difficult to fully assess the rigor of the study. Important elements such as participant characteristics, measurement procedures, and statistical analyses need clearer and more systematic explanation.

The presentation of results is not sufficiently clear, and the narrative does not always align with the data shown. Figures and tables require improved formatting and clearer captions to enhance readability. The conclusions are overstated relative to the evidence provided and should be more cautiously framed, strictly reflecting the results obtained. Additionally, the English language requires significant revision to improve clarity, grammar, and overall readability.

I encourage the authors to revise the manuscript thoroughly, strengthen the theoretical background, clarify the methodology, improve the presentation of results, and ensure that the conclusions are fully supported by the data. A careful language edit will also be necessary to meet the journal’s standards.

Author Response

REVIEWER 2

 

The manuscript addresses a relevant topic; however, substantial improvements are required before it can be considered for publication. The introduction does not provide sufficient background, and several key references in the field are missing. The rationale for the study is not clearly articulated, and the research questions are not well connected to the existing literature. The research design appears conceptually appropriate, but the methodological description lacks clarity and detail in several sections, making it difficult to fully assess the rigor of the study. Important elements such as participant characteristics, measurement procedures, and statistical analyses need clearer and more systematic explanation.

The presentation of results is not sufficiently clear, and the narrative does not always align with the data shown. Figures and tables require improved formatting and clearer captions to enhance readability. The conclusions are overstated relative to the evidence provided and should be more cautiously framed, strictly reflecting the results obtained. Additionally, the English language requires significant revision to improve clarity, grammar, and overall readability.

I encourage the authors to revise the manuscript thoroughly, strengthen the theoretical background, clarify the methodology, improve the presentation of results, and ensure that the conclusions are fully supported by the data. A careful language edit will also be necessary to meet the journal’s standards.

A: We sincerely thank the reviewer for the careful evaluation of our manuscript and for the constructive recommendations. In response, we conducted a comprehensive revision of the manuscript and substantially revised all major sections.

In the Introduction, we expanded the theoretical background, incorporated additional references, strengthened the rationale for distinguishing postural stability from strength-coordination, and clarified the study hypotheses within the context of current literature. Additional discussion was included regarding neurodevelopmental perspectives, embodied cognition, and the potential role of cerebellar-prefrontal networks in motor-cognitive associations.

In the Methods section, we provided more detailed descriptions of participant recruitment, sampling procedures, measurement protocols, executive-function assessment, motor-performance testing, and structural equation modeling procedures. We also expanded the explanation of model development, variable selection, and the handling of missing data, including a supplementary sensitivity analysis using Full Information Maximum Likelihood (FIML).

The Results section was revised extensively to improve clarity and consistency. All tables were carefully reviewed and corrected where necessary, including verification of parameter estimates, standard errors, z-values, and p-values against the original SEM outputs. Table formatting, captions, and supplementary materials were also revised to improve readability and transparency.

The Discussion and Conclusions were substantially revised to provide a more cautious interpretation of the findings. Greater emphasis was placed on effect sizes, explained variance, alternative explanations, residual confounding, measurement limitations, and the cross-sectional nature of the study. Language implying causal mechanisms or developmental influence was reduced, and indirect effects are now discussed as indirect statistical associations rather than causal pathways.

Finally, the manuscript was carefully revised to improve clarity, readability, consistency, and overall language quality throughout the text.

We believe these revisions have substantially strengthened the manuscript and have addressed the reviewer’s concerns regarding theoretical background, methodological transparency, presentation of results, interpretation of findings, and overall readability.

Reviewer 3 Report

Comments and Suggestions for Authors

Dear authors, 
thanks for your contribution for the promotion of heath. 
I found some items to be improved in the introductive paragraph.
First of all no studies were cited about what is discussed in lines 93-94.
The selection of the postural control as the main factor related to the executive function could be controversial.
For sure postural control requires what is describerd in your study but it was assessed by a steady state position while body control during motion is more related to the executive function (i.e. just-in-time adjustments, inhibition and control). 
In the Material and Methods paragraph I found a little missing (missing brachets in lines 117-118?).
Moreover I suggest to include teachers in order to have a better assessment for the executive functions because they are the ones that really face children' preschool expericence.
Parents could have only a general overview and less competence about the topic. 
For these reason I suggest to sumministrate the questionnaire to them too.
Anyway you in the section of comments you underlied the missing of quantified the executive function because it has been assessed by the parents only. 

Author Response

REVIEWER 3

Dear authors,

thanks for your contribution for the promotion of heath.

• I found some items to be improved in the introductive paragraph.

First of all no studies were cited about what is discussed in lines 93-94.

A: We thank the reviewer for this observation. We agree that the statement regarding the limited number of studies simultaneously examining these relationships should be better supported by the existing literature.

In response, we revised the Introduction to more clearly acknowledge previous research reporting associations between motor competence and executive functions while specifying the particular gap addressed by the present study. We also added citations to relevant previous studies and reviews. The revised text now clarifies that, although associations between motor competence and executive functioning have been documented, relatively few studies have simultaneously examined distinct motor domains, physical activity, anthropometric indicators, and executive functioning within a latent-variable framework.

• The selection of the postural control as the main factor related to the executive function could be controversial.

A: We thank the reviewer for this important observation. We agree that the relationship between specific motor domains and executive functioning remains an active area of investigation and that different motor components may contribute to executive functioning through distinct mechanisms.

The intention of the present study was not to assume a priori that postural stability is the most important motor domain for executive functioning. Rather, based on previous theoretical and empirical work, postural stability was selected as a domain of particular interest because balance-related tasks require continuous sensory integration, anticipatory regulation, error monitoring, and behavioral control processes that overlap conceptually with executive functions.

To clarify this rationale, we substantially expanded the theoretical background in the Introduction. Specifically, we incorporated additional discussion of neurodevelopmental and embodied-cognition perspectives, including evidence regarding the potential involvement of cerebellar-prefrontal networks, sensory integration processes, and the role of adaptive postural regulation in self-regulatory behavior. We also emphasize that the purpose of the study was to compare the associations of postural stability and strength-coordination with executive functioning within the same structural model, rather than to assume the superiority of one motor domain over another.

We believe these revisions provide a stronger theoretical justification for examining postural stability while acknowledging that other motor domains may also be relevant to executive functioning during early childhood.

• For sure postural control requires what is describerd in your study but it was assessed by a steady state position while body control during motion is more related to the executive function (i.e. just-in-time adjustments, inhibition and control).

A: We thank the reviewer for this insightful observation. We agree that dynamic forms of postural control may place additional demands on executive processes because they require continuous adaptation, online motor adjustments, inhibitory control, and regulation of movement in changing contexts.

In the present study, postural stability was assessed primarily through static balance tasks, which were selected because they are widely used and developmentally appropriate measures for preschool children. However, we acknowledge that dynamic balance and movement-based postural regulation may engage executive functions in somewhat different ways and could potentially show similar or even stronger associations with executive functioning.

To address this point, we expanded the Discussion to explicitly acknowledge that the postural-stability construct was based primarily on static balance measures and that dynamic forms of postural regulation may place additional demands on executive control. We further note that future research should examine whether dynamic balance and movement-based postural control exhibit similar or stronger associations with executive functioning during early childhood.

We appreciate this suggestion, as it provides an important perspective for interpreting the present findings and for guiding future research in this area.

• In the Material and Methods paragraph I found a little missing (missing brachets in lines 117-118?).

A: We thank the reviewer for identifying this typographical issue. The sentence was revised to correct the punctuation and parenthetical formatting of the ethics approval information. The revised text now clearly reports both the protocol code and approval date.

• Moreover I suggest to include teachers in order to have a better assessment for the executive functions because they are the ones that really face children' preschool expericence.

Parents could have only a general overview and less competence about the topic.

For these reason I suggest to sumministrate the questionnaire to them too.

Anyway you in the section of comments you underlied the missing of quantified the executive function because it has been assessed by the parents only.

 

A: We thank the reviewer for this valuable suggestion. We agree that teacher reports can provide important complementary information regarding children's executive functioning, particularly because teachers observe children in structured educational settings and across a wide range of cognitively demanding activities.

Unfortunately, teacher ratings were not available in the present dataset, and therefore it was not possible to incorporate an additional informant source in the current analyses. However, we acknowledge that relying exclusively on parent-reported executive-function difficulties represents a limitation of the study.

To address this point, we expanded the Limitations section to explicitly note that executive-function difficulties were reported exclusively by parents and that future studies would benefit from incorporating multiple informants, including teachers, who may provide complementary perspectives on children's everyday executive functioning in educational contexts. We also emphasize that future research would benefit from combining parent and teacher reports with performance-based executive-function assessments to obtain a more comprehensive evaluation of the construct.

We appreciate this recommendation and agree that a multi-informant approach represents an important direction for future research in this area.

Reviewer 4 Report

Comments and Suggestions for Authors

CHILDREN-4358302 presents findings for postural stability and executive functions in preschool aged children. My comments are minor.

• Table 1: Just present mean and standard deviation. Having additional measures of variability is not needed and this can be kept in house to determine stuff like outliers.
• Discussion: Postural stability could also be related to dual tasking and neuromuscular control, which is likewise linked to cognitive function. Some text edits to mention might be warranted.
• Make any changes to the abstract that align with those from the text.

Author Response

REVIEWER 4

CHILDREN-4358302 presents findings for postural stability and executive functions in preschool aged children. My comments are minor.

• Table 1: Just present mean and standard deviation. Having additional measures of variability is not needed and this can be kept in house to determine stuff like outliers.

A: We thank the reviewer for this suggestion. In response, Table 1 was simplified to present descriptive data as means and standard deviations only. Additional descriptive statistics that were included for internal data screening purposes were removed to improve clarity and readability.

• Discussion: Postural stability could also be related to dual tasking and neuromuscular control, which is likewise linked to cognitive function. Some text edits to mention might be warranted.

A: We thank the reviewer for this helpful suggestion. We agree that postural stability may also reflect aspects of neuromuscular control and dual-task processing, both of which have been linked to cognitive functioning. To acknowledge this perspective, we expanded the Discussion to note that neuromuscular control and dual-task demands may represent additional mechanisms contributing to the observed association between postural stability and executive functioning.

• Make any changes to the abstract that align with those from the text.

A: We thank the reviewer for this recommendation. The Abstract was carefully revised to ensure consistency with the changes made throughout the manuscript. In particular, the wording was updated to reflect the more cautious interpretation of cross-sectional associations, indirect effects, and the overall conclusions of the study.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Authors have done well job on revising their manuscript.