These authors used longitudinal data from a large sample of mothers and fathers in China to examine associations among parent involvement and child social competence. The manuscript was compelling and the use of the actor-partner interdependence model was a real strength. These comments are offered with the goal of making for a stronger final publication.

Maybe mention the actor-partner interdependence approach in the title.

The sample size was unclear. The authors mention 1880 in the abstract but 2158 is referred to as the “final sample” on page 11. Also, the sample should provide some indication of the average child age at times 1 and 3.

The final page 4 paragraph indicates that father involvement has been studied more than mother involvement, however, this is contrary to my understanding of the literature where fathers are considerably less likely to be studied than mothers. After a bit of research, I found that indeed “father involvement” appears more often in PsychInfo than “mother involvement”, respectively, with 1400 citations for fathers and 184 for mother involvement. Narrowing my search, I found mother was cited 138,995 compared to 62,014 citations for fathers. It might be helpful for readers to be reminded that father involvement is studied more than mother involvement.

On page five the authors noted that “…father involvement activities may not have a significant impact on…”, however, null hypothesis significance testing principals suggest the authors should more accurately claim that “…no evidence suggests father involvement activities have a significant impact on…”.

Later, on page five, the authors describe a study that “…focused on father involvement over mother involvement…” Are the authors describing a study that examined the additive contributions of mothers and fathers?

In the closing paragraph of page seven, the authors refer to the APIM for the third time in the introduction and talk about the potential for future research. Given that these researchers already conducted this work, references to future research are confusing.

At eight pages, the introduction is a bit long and repetitive. One section that needs to be added, however, is a current study section on page 10 to prepare readers for the hypotheses that will be tested. The authors organize their results around hypotheses so sharing them before explaining the method will be helpful.

The research team did a wonderful job of retaining such a large sample. That said, were there attrition effects on the main study variables for the sample of 2164 at time 1 compared to the 1985 retained at time 3? Alternatively, maybe compare the 2158 versus the 1880. The authors kind of address this in the second paragraph of page 13, however, mean differences (compared to differences in associations) might be of interest.

For the main study measures, who were the reporters? Did fathers report on mother involvement and vice versa? Did both parents report on child social competence? Additionally, who reported on the control variables?

For Table 1, add a note to explain what T1, T2, and T3 abbreviate.

Figures 2 and 3 would benefit from a note to explain what each of the p values indicate in terms of asterisks.

Closer attention to APA style would offer greater face validity to the manuscript. Some examples:
• The title of the paper should appear at the beginning of the introduction.
• Numbering the sections isn’t part of level headings.
• When the authors describe variable value labels, the value labels should be italicized and not placed between quotation marks.
• On page 12, zero values should not proceed the alpha value because alpha cannot be greater than one.

Reviewed by Jeff Cookston

In this revision, the authors have mostly addressed reviewer suggestions and the manuscript is much stronger. The changes below are offered to improve the manuscript.

First, I suggest replacing the word “in” with “among” in the title and throughout the paper (e.g., p. 4).

The abstract could use more detail. Maybe add that social competence was measured with a latent variable. Also, add more of the unsurprising results such as the finding that all three constructs were stable over time in the APIM. Additionally, mention that no evidence was found linking MI or PI to social competence.

At times, the authors write about family experiences in very scientific manners. For example, on page 3 the authors refer to involvement as a “construct” and on page 4 when they refer to “the delivery of caregiving services” or on page 6 when they refer to “children’s characteristics and behaviors”.

Remove the second reference to Kraemer et al. 2020 on page 5. It’s redundant as the citation is noted in the prior sentence.

On page 5 the authors say “Another explanation pertains…” but it’s an explanation for what?

On page 7, the authors refer to White people as Caucasian. The seventh edition of the APA style manual has clearly directed us to retire this racist reference to people raised to believe themselves to be White. Just say White even if Barbot et al. 2014 didn’t.

On page 9 the authors note “This study examines…” when they should have written in the past tense by saying examined. The authors should also use the past tense on page 12 when they described how constructs were measured.

On page 9 the authors say utilized when used is the correct word.

For involvement, how were the items scored – a sum of the items or a mean score?

In Table 2 was social competence a composite score? How did they correlate the latent variable of social competence with the measured indicators of parenting?

Child gender, SES, and age should be added to Table 2.

On page 14 the authors detail a number of statistical and model configurations that merit a citation to a methodological paper.

While beyond the scope of this paper possibly, it would be interesting to know if the final model works the same for boys and girls. Possibly mentioning this in the discussion section would be of value.

Reviewed by Jeff Cookston

This version of the manuscript has been adequately revised and is ready for publication. The remaining suggestions I would offer can be fixed by the copy editing team per the editor's expectations.