Overview
Thank you for the opportunity to review this manuscript regarding the longitudinal associations between maternal and paternal involvement on child social competence. This manuscript has the potential to add to the current literature on parental involvement by using a family approach. There are some concerns about the strong language used and flow of the introduction and discussion that detract from the overall findings of this study. Suggestions are included below that are intended to help give the manuscript a stronger argument and more impactful.

Introduction
1. This sample is a Chinese sample, but it does not come up until page 9. It is vital to this paper to clearly explain in the first couple paragraphs why this question should be asked in this population. There might be a good reason to study this question in this population given distinct cultural characteristics, but that is not explained at all.
a. Related, it would be beneficial to understand and clarify which samples are European/US samples versus non-white samples to get a better understanding of the literature. Especially when there are strong assertions made when the results are different.
2. The current definition of involvement is vague and could be applied to most parenting behaviors. The manuscript also does not make clear the importance of studying (1) involvement versus specific parenting behaviors and (2) global involvement versus specific types of involvement. A definition is vital given that the manuscript discusses research that looks at involvement in different ways and there needs to be a better discussion of why more global assessments of involvement are important.
a. Additionally, a better argument should be made for why maternal involvement needs to be studied as most studies look at maternal parenting behaviors.
3. There are numerous mentions of inconsistencies in the research (page 5, line 45-49; page 6, line 29-34; page 9, lines 15-20, line 22), but there is no reporting of studies that find null or opposite effects. It is fine to make these conclusions, but the manuscript needs to at least cite the studies that have yielded different results. Otherwise, these sentences need to be changed.
4. There are some issues with flow that should be addressed to strengthen the paper.
a. It is unclear why attachment theory is discussed in such detail as this would seem to allude more to specific parenting behaviors, as written. Involvement alone does not inform attachment by itself. This should be more carefully framed to suggest this is one possible reason why involvement matters as it relates to social competence.
b. The Cabrera heuristic (and the entire paragraph) should be moved into the previous paragraph to give a stronger argument for reciprocal effects. Additionally, the transactional model is not just an assertion that children influence parents, but the reciprocal effects between parent and child.
c. The manuscript brings in family systems theory (page 6, line 33) that should be made into a separate paragraph.
d. Discussion of multiple theories (gate-keeping, demand response capacity) to describe mother father influence on each other. The manuscript should just stick with the one that is aligned with their hypotheses.
e. Page 8 – The section on child influences on parenting involvement is hard to follow. The detail provided for educational involvement seems tangential to the global measure this study uses. It would be more beneficial to highlight key findings in a few sentences (related to inconsistencies more broadly) or make it clear that one paragraph is about positive effects of involvement and the other negative effects.
i. It is also unclear why Lindsey (1997) is included here. The set up is hard to follow
f. Discussion of APIM (page 7) should be moved to the analysis plan section.
5. Page 4 lines 31-38 is a direct quote from Pleck 2007 and is not treated as such. Please either correctly refer to this (quotes, indention, etc.) or paraphrase.
a. Related to Pleck, 2007. This article only discusses fathers but is being cited for both mothers and fathers. Please either cite additional work or rework this sentence.
6. Page 5 lines 31-33: “Compared to longitudinal design, the cross-sectional… drawing confident causal conclusions”. Even longitudinal designs cannot draw “causal” conclusions. This is not an experiment and so these are still just associations. This language needs to be adjusted, and the citation currently used should be removed as it is not a methodological paper about causality.
a. Also found in the discussion - Page 19 – “…which allowed for more solid conclusions…”. The citation of Daniel et al., 2016 is not a methodological paper on longitudinal designs and causality. Please fix the language.
7. Citations are being used to represent ideas that are not based on those citations.
a. Family Systems Theory should reflect those (Cox & Paley; Minuchin) who conceptualized this theory versus another manuscript that used this theory.
b. Yoleri (2023) does not seem to be related to this study given their examination of temperament and not social competence.
8. This manuscript is missing a current study section. The manuscript includes what the current study will be doing in each paragraph and instead should move all of that to a section “current study” to address the gaps in one cohesive place.
a. Please add in hypotheses or research questions that guided this work to better connect with the analyses.

Methods
1. Most statistics reported are for the larger study that this study came from (including age and attrition). This paper instead should focus on reporting the child age at each wave and attrition for this study specifically.
a. Also, either present further demographic information on the parents in text or as a table (parent age, education level, occupation, etc.).
2. If an inclusion criterion was that the parents were married, why are the percentages not 100%?
3. What scales were used for involvement and social competence.
a. It is not clear in the discussion of involvement whether the scale was a total of 5 items pulled from these specific areas or 5 items for each area. Please clarify.
4. An attrition analysis needs to be conducted for this missing data.
5. Please report how mediation analyses were tested.

Results
6. It is not clear why separate mother and father models were run. The argument throughout the manuscript was that mother and father should be looked at together. It is recommended that the mother and father model be removed and only the full model be presented particularly given that there is no added benefit to including these models.
7. There is no presentation of the other models (tables, discussion of decisions) that were run aside from the final models. For example, a sentence stated that paths were set to equality without an explanation or report that this nested model was tested.
8. Figures – correlations should be represented as curved arrows instead of the current bidirectional arrows.
9. Page 13, it is not clear what this sentence means “The findings in this subsample were similar to those in the total sample.” The total sample of KIT? If so, why is this subsample being shown and then future directions are to look at all family types?
a. It states there are supplementary materials, but none are provided.
10. Page 13, line 15: “Moreover, this study estimated…., indicating.” There are words likely missing here. It should read that the interactions were non-significant, indicating that… .
a. Also, an interaction effect was not discussed as a part of the study. Please provide rationale for looking at this interaction.
11. Page 16 “…suggesting that maternal involvement and paternal involvement were differently connected to other constructs” this sentence needs to be clarified instead of saying “other constructs”.

Discussion
2. The transactional model is used to describe the impact of child on parents – this is not evidence of the transactional model. The transactional model is when there are bidirectional effects which were not found. Please adjust and discuss how this is not evidence of the transactional model.
3. The manuscript needs to make a clearer connection to the Chinese culture and why the results support it (page 18). Currently, the discussion weaves non-Chinese sample results with Chinese culture making it difficult to follow.
a. Language like “Naturally, Chinese fathers and mothers are willing…” without support is too strong.
4. Strong statements are made throughout the discussion with no support and need to be fixed (examples below).
a. Page 20 - “mothers usually prefer…” this is not what this study stated and also using the incorrect citation (citing one paper instead of the source material).
b. Page 19 “Here are reasons why …” – change to potential reasons because it is not known.
5. This manuscript makes an argument that fathers are more involved when the mothers work. This analysis controlled for occupation in your models (with SES), so this could not be an explanation for your findings.
6. Torres et al., (2014) does not talk about reproductive strategy as it relates to mothers and fathers, but only fathers (page 18). Please adjust or better explain the connection to mothers as well.
7. Paragraph 2 on page 19 briefly mentions that children are not passive recipients, and it is unclear how this fits in with the rest of the paragraph.
8. In the final conclusions, there is no discussion of these paper’s findings and reverts to what previous studies found. If the results from this study are presumed to be unique the final conclusions should reflect that.

I appreciate the authors high level of responsiveness to feedback, addressing comments thoughtfully. Their revisions reflect a clear commitment to improving the work based on constructive input. I believe that this paper can be very informative particularly its findings of child driven effects on parental involvement.

One final revision based on the changes made is to change "predict" used in the manuscript to "associate, related to", etc., as predict should not be used in a non-causal study.