Parental Reflective Functioning in First-Time Parents and Associations with Infant Socioemotional Development

Parental reflective functioning (PRF) refers to parents’ capacity to reflect on mental states such as their own and their child’s feelings, thoughts, and intentions. Studies suggest that PRF is an important factor in parental behavior; however, only a few studies have examined the effect of early PRF on infant socioemotional development. The Parental Reflective Functioning Questionnaire (PRFQ) was developed as a brief, multidimensional measure to assess PRF. Recently, a modified version, the PRFQ-I, was suggested as a more accurate measure of PRF in an at-risk sample of mothers of infants. The study aims were to examine the factor structure and factorial invariance across parental gender of the PRFQ-I in a community sample, to compare PRF dimensions across mothers and fathers, and to investigate the association between PRF dimensions and infant socioemotional development. We examined this within a longitudinal design in a community sample of 1243 first-time mothers and 512 fathers. The results supported the expected factor structure of PRFQ-I and invariance across parental gender. Significant differences between mothers and fathers were found on the three PRF dimensions comprised by the questionnaire. The PRF dimensions of pre-mentalizing and certainty about mental states significantly predicted infant socioemotional development. Findings show that the PRFQ-I is a valid measure in parents of infants and suggest that PRF in early parenthood is an important factor in infant socioemotional development. Identification of first-time parents with limited PRF enables early intervention and may thus prevent limited PRF from having potentially adverse effects on infant socioemotional development. The factor structure of the Parental Reflective Functioning Questionnaire, Infant version, was an acceptable fit in a community sample of parents 4 months postpartum. Measurement invariance across mothers and fathers was achieved at the configural, metric, and scalar level. Mothers reported lower levels of pre-mentalizing and higher levels of certainty about mental states, and interest and curiosity than fathers. Pre-mentalizing and certainty about mental states at 4 months predicted infant socioemotional development at 11 months. The factor structure of the Parental Reflective Functioning Questionnaire, Infant version, was an acceptable fit in a community sample of parents 4 months postpartum. Measurement invariance across mothers and fathers was achieved at the configural, metric, and scalar level. Mothers reported lower levels of pre-mentalizing and higher levels of certainty about mental states, and interest and curiosity than fathers. Pre-mentalizing and certainty about mental states at 4 months predicted infant socioemotional development at 11 months.

The factor structure of the Parental Reflective Functioning Questionnaire, Infant version, was an acceptable fit in a community sample of parents 4 months postpartum.
• Measurement invariance across mothers and fathers was achieved at the configural, metric, and scalar level.
• Mothers reported lower levels of pre-mentalizing and higher levels of certainty about mental states, and interest and curiosity than fathers.
• Pre-mentalizing and certainty about mental states at 4 months predicted infant socioemotional development at 11 months.
Parental reflective functioning (PRF) or parental mentalization refers to a parent's capacity to reflect on the mental states of oneself as a parent as well as those of the child, and to understand that mental states such as feelings, thoughts, and intentions affect a child's behavior Slade, 2005). The parental ability to perceive infant behavioral cues and to understand and interpret the underlying mental states is crucial for parents to respond sensitively and appropriately to the childperhaps especially during infancy when parent and infant mainly communicate non-verbally . Research supports this notion; parental mentalization has been related to parental behavior such as sensitivity  and to child outcomes such as socioemotional development (Camoirano, 2017;Ensink et al., 2016;Gordo et al., 2020) and child attachment (Ensink et al., 2017;. Several measures such as interviews and questionnaires are available for assessing PRF (Anis et al., 2020;Schiborr et al., 2013). The Parental Reflective Functioning Questionnaire (PRFQ) is a time-and cost-efficient 18-item instrument for measuring PRF in parents of children aged 0-5 years  that has generally shown good validity and reliability (Anis et al., 2020;Rutherford et al., 2015). In contrast to other measures, yielding a global score of PRF, the PRFQ is multidimensional, measuring three dimensions of PRF. (1) Pre-mentalizing (PM) is defined as limited mentalizing or a non-mentalizing stance, where the parent makes maladaptive and malevolent attributions about the child's mental states (e.g., "My child cries around strangers to embarrass me"). Low scores on this dimension characterize optimal PRF. (2) Certainty about Mental States (CMS) is defined as the level of certainty in attributing mental states to the child and the recognition of the opacity of mental states (e.g., "I can completely read my child's mind"). Low scores reflect hypomentalizing, where the parent is overly uncertain about the child's mental states, whereas high scores could reflect hypermentalizing, where the parent fails to recognize the opaqueness of mental states. Thus, medium scores on this dimension characterize optimal PRF. (3) Interest and Curiosity (IC) in infant mental states is defined as the parent's curiosity in and active willingness to understand the child's mental states (e.g., "I am often curious to find out how my child feels"). Low scores on this dimension indicate hypomentalizing, reflecting a lack of interest in the child's mental states, whereas some studies suggest that very high scores might indicate hypermentalizing, reflecting an excessive or intrusive interest in the child's mental states. Thus, medium to high scores on this dimension characterize optimal PRF .

Development of the PRFQ-Infant
The PRFQ was designed to capture PRF in parents of children aged 0-5 years , but due to the large developmental differences within this age span, parental mentalization may change according to the age of the child. In infancy, PRF relies solely on the parent's ability to interpret nonverbal and behavioral cues and signals, whereas with the acquisition of language, the child becomes able to more directly express his or her mental states verbally . Furthermore, when it comes to infants and toddlers, the relationship between the parent and the child is still evolving, and PRF may become more refined over time as the relationship develops (Rutherford et al., 2015;Slade, 2005). In a recent study examining associations between child age, child emotion regulation and maternal mentalization, PRFQ was used to measure PRF in a sample of mothers of children aged 0-8 months, 9-14 months, 15-20 months, and 21-26 months (Àlvarez et al., 2022). The results of this study showed a significant negative association between child age and the PM subscale of the PRFQ, suggesting that the tendency to make maladaptive and malevolent attributions about the child's mental states diminishes as the child grows older.
Based on the above, it seems plausible that PRF in parents of infants differs from that in parents of older children, and that PRF in early parenthood may be better captured by another factor structure of the PRFQ. In a recent study, Wendelboe et al. (2021) examined this hypothesis in a sample of 423 mothers, 237 of whom met the diagnostic criteria for a current major depressive episode (PPD group) and 186 who did not (no-PPD group). The mothers in the study completed the PRFQ when their children were 1-11 months old, with 89% of the children aged 0-5 months. The purpose of the study was to investigate the factor structure of the PRFQ, with a confirmatory factor analysis (CFA) being conducted in the two groups separately to examine the fit of the model in both groups. The initial results of the CFA showed a poor fit in both groups, with three of the items not loading significantly on the PM subscale. Hence, these three items were removed, and a modified 15-item model was tested with CFA in both groups. This model showed an excellent fit in the no-PPD group, and after one error covariance was added, it also showed an excellent fit in the PPD group. The shortened version of the scale was termed PRFQ-Infant (PRFQ-I) but to our knowledge, this version of the scale has not yet been used or validated in other studies. Hence, there is a need to examine whether the PRFQ-I factor structure can be replicated in other samples.

Similarities and Differences in PRF Between Mothers and Fathers
Previously, the majority of the PRF literature has focused on mothers (Camoirano, 2017), but an increasing number of studies include fathers as well, which enables the PRF of mothers and fathers to be compared. Studies employing the PRFQ show that while mothers and fathers tend to score equally high on the CMS subscale, fathers tend to score higher on the PM subscale and mothers tend to score higher on the IC subscale (Cooke et al., 2017;Gordo et al., 2020;Pazzagli et al., 2018). This suggests that mothers' and fathers' scores need to be examined separately when the PRFQ is used.
In order to validly examine and compare different group means, Putnick and Bornstein (2016) stressed the importance of examining measurement invariance (MI) beforehand. An examination of MI tests whether a latent construct (here PRF) holds the same measurement structures across groups (Van De Schoot et al., 2015), indicating that the associations between the PRFQ items and the latent construct do not depend on group membership. Hence, prior to testing differences between mothers and fathers on the PRF dimensions, it is important to examine whether the measurement instrument captures the same underlying construct of PRF for both mothers and fathers. If MI does not hold, any observed differences between mothers and fathers are due to measurement differences and not to true underlying differences on the PRF construct. If MI does hold, (mean) scores between mothers and fathers can be meaningfully compared, as they represent the same underlying PRF construct (Van de Schoot et al., 2012). With regard to the PRFQ, a number of studies have examined MI between mothers and fathers (e.g., De Roo et al., 2019;Pazzagli et al., 2018;Ye et al., 2022), with the results from these studies generally supporting the existence of MI between mothers and fathers. However, MI has not yet been examined with the PRFQ-I.

Parental Mentalization and Child Socioemotional Development
Parental mentalization is important for child socioemotional development. When measured as a unidimensional construct, parental mentalization has been found to promote attachment security and the ability to regulate emotions, and increases the understanding of one's own and others' mental states (Camoirano, 2017: Ensink et al., 2016Esbjørn et al., 2013;Heron-Delaney et al., 2016;Salo et al., 2021;Slade et al., 2005;Smaling et al., 2017;Zeegers et al., 2017).
Although when measured as a unidimensional construct, parental mentalization has been found to be related to child socioemotional development, recent research indicates the need to perceive PRF as a multidimensional construct to disentangle the effects of the different dimensions of PRF on child socioemotional development (Smaling et al., 2017). However, to date only two studies (Gordo et al., 2020 andNijssens et al., 2020) have examined how the different dimensions of PRF relate to child socioemotional development. Gordo et al. (2020) examined the relationship between PRF and child socioemotional development in a crosssectional study of 433 mothers and 113 fathers of infants aged 2-36 months (M = 16 months). They used the PRFQ to assess PRF, and the Ages & Stages Questionnaires: Social-Emotional, Second Edition (ASQ:SE-2; Squires et al., 2015) to assess child socioemotional development. When including both mother and fathers in the analysis, they found that all three PRF subscales correlated with child socioemotional development. Furthermore, they found that pre-mentalizing had a direct negative effect on child socioemotional adjustment and an indirect effect through parental competence, while certainty about mental states and interest and curiosity affected child socioemotional adjustment indirectly through parental competence (Gordo et al., 2020). These results were similar when examining mothers and fathers separately.
As part of a longitudinal study, Nijssens et al. (2020) examined the relation between PRF in mothers and fathers and infant socioemotional development in a sample of 53 couples with children aged 19-26 months. PRF and child socioemotional development were both measured at the second time point of the study using the PRFQ and the Brief Infant-Toddler Social and Emotional Assessment (BITSEA; Briggs-Gowan & Carter, 2002), respectively. The results of this study showed that higher levels of pre-mentalizing in mothers and fathers, when measured separately, were associated with lower child socioemotional adjustment while certainty about mental states and interest and curiosity were not associated with child socioemotional development (Nijssens et al., 2020).
To sum up, although research where PRF is measured as a unidimensional construct has consistently found PRF to be related to child socioemotional development, knowledge about how the different dimensions of PRF are related to child socioemotional development is still sparse. Results from the two studies examining multidimensional PRF and child socioemotional development showed that higher levels of pre-mentalizing negatively affected child socioemotional development (Gordo et al., 2020;Nijssens et al., 2020), but the results regarding the associations between certainty about mental states and interest and curiosity and child socioemotional development were mixed. One study showed indirect effects on child socioemotional development through parental competence (Gordo et al., 2020), and the other study showed no effects (Nijssens et al., 2020). These differences might partly be due to the different measures used to assess child socioemotional development in the two studies (ASQ:SE-2 and BITSEA), but the differing findings also suggest that more studies are needed in this area.

The Present Study
In the present study, we aim to 1) test the factor structure and cross-gender measurement invariance of the PRFQ-I in first-time mothers and fathers of infants aged 4 months, 2) compare levels of PRF dimensions across parental gender, and 3) estimate the associations between PRF dimensions at 4 months and parental reports of infant socioemotional development at 11 months. As regards to aim 1, we hypothesize that we will find a three-factor model including pre-mentalizing, certainty about mental states, and interest and curiosity in both mothers and fathers to be an adequate fit, and that the model will show measurement invariance across parental gender. In relation to aim 2, we hypothesize that mothers will report higher levels of interest and curiosity than fathers, and that fathers will report higher levels of pre-mentalizing. We do not expect to find parental gender differences regarding certainty about mental states. For aim 3, we hypothesize that after controlling for parental education, pre-mentalizing in mothers and fathers, measured separately at 4 months postpartum, will predict infant socioemotional development at 11 months. Specifically, we expect higher levels of pre-mentalizing to significantly predict lower levels of infant socioemotional adjustment. Based on findings from previous studies, we do not expect to find the effects of the other PRF dimensions on infant socioemotional development.

Procedure
The present study was part of a larger intervention study, Understanding Your baby, focusing on the experiences of first-time parents in the first year of parenthood and on the efficacy of a universal parenting program delivered by health visitors in a primary care setting (the study was registered at clinicaltrials.gov with registration no. NCT03991416). The aim of the parenting program was to promote parental competence by supporting new parents in noticing their infant's behavioral cues and interpreting them in terms of mental states. The intervention was delivered by health visitors, who described specific infant behaviors and helped the parent interpret these behaviors in terms of social and emotional needs during a routine observation of infant social withdrawal. The intervention study was a controlled parallel group study, with the participants in the present study being part of the baseline sample that did not receive the parenting program. The intervention study was performed in line with the principles of the Declaration of Helsinki. Approval was granted by the Institutional Review Board at the Department of Psychology, with approval number IP-IRB / 23112018 (23/11-2018). Informed consent was obtained from all individual participants included in the study.

Participants
In the baseline sample, all registered first-time mothers giving birth from April 2019 to September 2019 from 26 Danish municipalities were invited to participate in the study if they were at least 18 years old when the child was born and living together with the child. The other parent was invited if the parent was at least 18 years old and living together with the child or living in the same municipality as the child. Parents with twins or parents who were legally incapacitated were not invited. All parents received the invitation via a secure public email service.
In total, 6337 mothers and 5078 registered other parents were invited to participate and, of those, 2015 mothers (32%) and 1001 registered other parents (19%) consented to participate. The participating parents received a set of questionnaires at four time points during the first year of parenthood: 2 months (T1), 4 months (T2), 7 months (T3), and 11 months (T4) after birth. Data from T1, T2, and T4 were used for the current study. To examine differences between mothers and fathers, we only included registered other parents who were males. For the analyses, we only included participants who had complete data from all three time points, resulting in a final sample of 1243 mothers and 512 fathers (see response bias analysis in Table 1). In 242 cases, both the mother and the father of the same child participated in the study, meaning that 1001 (80.5%) of the mothers and 270 (52.7%) of the fathers participated in the study without the other parent participating. REDCap electronic data capture tools were used to send out and manage the questionnaires (Harris et al., 2019;Harris et al., 2009). Each time the parent answered a set of questionnaires, he or she had the opportunity to participate in a draw for a gift certificate with a value of DKK 500 (approx. USD 80) for a baby store. If the parent completed all four sets of questionnaires, a children's book at a value of DKK 70 (approx. USD 11) was sent to the parent. The PM factor consists of three items (omitting items 7, 10, and 13 from the original 18-item PRFQ) and reflects a tendency to ascribe malevolent attributions to the infant and a lack of ability to take an intentional stance towards the infant (e.g., "Often, my child's behavior is too confusing to bother figuring out"; . The CMS factor consists of the original six items from the PRFQ and relates to the parental ability to recognize the opaqueness and uncertainty of infant mental states (e.g., "I always know what my child wants"). The IC factor also contains the original six items from the PRFQ and reflects genuine parental interest in and curiosity about, infant mental states (e.g., "I am often curious to find out how my child feels"). The items are rated on a 7-point Likert scale ranging from 1 (completely disagree) to 7 (completely agree). The PRFQ-I was administered to the parents at T2. The Cronbach's alphas for the PRFQ-I in the current study for mothers/ fathers were .40/.43 for the PM subscale, 0.84/0.82 for the CMS subscale, and .70/.70 for the IC subscale.

Infant socioemotional development
The Danish version of the Ages & Stages Questionnaires: Social-Emotional, Second Edition (ASQ:SE-2, Squires et al., 2015) was used to measure infant socioemotional development. In this study, we used the version targeting parents with children aged 9-14 months. The ASQ:SE-2 contains 27 items assessing parental reports of five developmental areas with the aim of identifying children at risk of social or emotional problems. The five areas are Response bias analyses on categorical variables were conducted using chi-square statistics, while continuous variables were examined using independent t-test analyses between groups. The analyses revealed no significant differences between respondents and non-respondents. Response bias analyses were not conducted for parental leave, because these data were collected at T4 self-regulation, adaptive functioning, affect, social communication and interaction. Examples of statements are "When you talk to your baby, does he turn his head, look, or smile?", "Does your baby like to be picked up and held?" and "Does your baby look for you when a stranger comes near?" The items are rated on a 3-point Likert scale with 1 (often or always = 10 points), 2 (sometimes = 5 points), and 3 (rarely or never = 0 points). In addition to this, parents check off whether they find the item-specific behavior a concern (adding 5 points). ASQ:SE-2 was completed at T4 approximately 11 months postpartum. In our analyses, we used the total score continuously, in which higher scores indicate higher levels of infant socioemotional maladjustment. ASQ:SE-2 has shown good validity and reliability (Squires et al., 2015) and generally shows good internal consistency, although lower levels have often been found in samples with infants below 14 months (Salomonsson & Sleed, 2010). In the current study, Cronbach's alphas for the ASQ:SE-2 12-month interval scale were .62 for mothers and .67 for fathers.

Demographic background
At T1, when the infants were 2 months old, the parents answered several demographic background questions regarding parental age, education, ethnicity, employment status, partner status, whether the pregnancy was planned or not, and child characteristics. At T4, the parents completed a short questionnaire regarding breastfeeding and parental leave in the previous year.

Statistical Analyses
Initially, we conducted response bias analyses on sociodemographic variables between participants with complete data (respondents) and participants with missing data at T2 and/or T4 (non-respondents) to examine potential attrition bias. Prior to the analyses, we checked data for outliers and normality. The PM and IC subscales indicated non-normality at item and scale level. To account for this in the analyses, we used maximum likelihood with robust standard errors (MLR). First, we conducted a confirmatory factor analysis (CFA) to test the fit of the suggested modified 15-item factor structure of the PRFQ-I (Wendelboe et al., 2021). Next, we conducted a measurement invariance analysis across parental gender. Specifically, we conducted a series of tests examining increasingly restrictive levels of measurement invariance (Putnick & Bornstein, 2016;Van de Schoot et al., 2012). These levels include configural (does the same item measure the same construct?), metric (are factor loadings equivalent?), scalar (are factor loadings and intercepts equivalent?) and residual (are factor loadings, intercepts and residual errors equivalent?) invariance. Each model builds on the previous one, so once configural invariance has been established, a metric invariance model is tested against it and so on (Putnick & Bornstein, 2016).
The recommended fit indices used to assess model fit for CFA and multi-group CFA are the chi-square (χ2) statistic, comparative fit indices (CFI), root mean square error of approximation (RMSEA), and standardized root-meansquare residual (SRMR). The chi-square (χ2) statistic is sample-size sensitive (Chen, 2007;Putnick & Bornstein, 2016), resulting in a tendency of rejection of acceptable models in the case of a sufficiently large sample size, such as in the present study. Thus, for evaluation of model fit we relied on a combination of alternative fit indices: CFI, RMSEA, and SRMR (Chen, 2007). For a model to have an adequate fit, the fit indices should be CFI > 0.90, RMSEA < 0.08 and SRMR < 0.08. With CFI > 0.95 and RMSEA < 0.06 the model has a good fit (Bentler & Satorra, 2010;Browne & Cudeck, 1992;Chen, 2007). Chen (2007) suggested the following standards for cutoff criteria testing for multigroup invariance that we used in this study: to test invariance, cutoff criteria of a change in model Remaining estimates are statistically significant at the p < 0.001 level. The added residual error covariance between item 16 and item 18 is presented in the model fit of ≥0.010 for the ΔCFI, ≥0.015 for the ΔRMSEA, and ≥0.030 for the ΔSRMR were suggested as indications of noninvariance (Chen, 2007). As SRMR is more sensitive, different values are suggested for this index at different levels of invariance (Chen, 2007). Thus, for scalar and residual invariance testing, the cutoff criteria of ≥0.015 for the ΔSRMR are recommended, whereas the cutoffs for ΔCFI and ΔRMSEA are the same as before.
Then, to examine potential differences and similarities in the dimensions of PRF in first-time mothers and fathers, we calculated Pearson's correlations between the main variables, and conducted an independent samples t-test to compare PRF scores between mothers and fathers.
For our last aim, we applied a multiple regression model to examine whether PRF dimensions, reflected by the subscales of PM, CMS, and IC, predict infant socioemotional development. This was done separately for mothers and fathers. Parental education level was included as a control variable following previous research showing that higher levels of parental education are positively related to PRF (Cooke et al., 2017;Pajulo et al., 2018).

Descriptive
The sociodemographic characteristics of the sample are reported in Table 1. Of the 1557 mothers and 668 fathers responding at T1, 324 (20.7%) mothers and 156 (23.4%) fathers did not respond at T2 and/or T4. Response bias analyses revealed no significant differences between respondents and non-respondents (Table 1). Compared with the general Danish population (Statistics Denmark, 2021), a larger percentage of the parents in the current sample were of Danish origin, with 90.6% of the mothers in the sample being of Danish origin compared with 79.1% of all Danish women aged 20-49 years, and 91.4% of the fathers in the sample being of Danish origin compared with 82.7% of all Danish men aged 20-64 years. Furthermore, the parents in the current sample had a much higher level of education compared with the general population (Statistics Denmark, 2021). Of the mothers in the sample, 40.2% had a master's degree or higher compared with 16.6% of all Danish women aged 20-49 years, and 43.6% of the fathers in the sample had a master's degree or higher, compared with 12.6 % of all Danish men aged 20-64 years.

Confirmatory Factor Analyses and Measurement Invariance
The fit indices for the proposed three-factor model of the PRFQ-I for the mothers were CFI = 0.935, RMSEA = 0.049 [0.043, 0.054], and SRMR = 0.047, and for the fathers: CFI = 0.899, RMSEA = 0.062 [0.053, 0.071], and SRMR = 0.056. After inspecting the modification indices, we added one theoretically meaningful residual error covariance between item 18 and item 16 in the model. Item 18 states "I believe there is no point in trying to guess what my child feels" and loads on the IC factor, while item 16 states "Often, my child's behavior is too confusing to bother figuring out" and loads on the PM factor. Item 18 is reverse scored, in that a higher score on this item is related to less interest and curiosity. Although the two items load on different subscales, they have a similar semantic structure and reflect a lack of parental mentalization. However, the two statements also represent different aspects of low parental mentalization in that item 18 reflects an unwillingness or a lack of genuine interest and curiosity to take a mentalizing stance, while item 16 reflects an avoidance or an inability to even try to attribute realistic mental states to the child's behavior. Thus, it is possible that the two items share measurement variance and can be suggested to be separate statements of low parental mentalization, which may be allowed to correlate. When this modification was included, the model fit improved for both mothers and fathers. The fit indices for the final modified models with added residual error covariance between items 16 and 18 are presented in Table 2 for both mothers and fathers.
Except from the significant chi-square values, an evaluation of fit indices suggested that the PRFQ-I was an adequate fit for the present sample of first-time mothers and fathers with the fit indices CFI > 0.90, RMSEA < 0.08, and SRMR < 0.08. Factor loadings for the final modified model for mothers and fathers are reported in Fig. 1. All factor loadings were significant and ranged between 0.20 and 0.82 for the mothers, and 0.20 and 0.80 for the fathers. Results showed that items 1 and 4 on the PM subscale, items 11 on the CMS subscale, and items 15 and 18 on the IC subscale had relatively low factor loadings.
We then examined measurement invariance across mothers and fathers. The results are reported in Table 3 and show measurement invariance across parental gender at the configural, metric, and scalar level. Residual measurement invariance was not achieved. This level of invariance is not a prerequisite for comparing mean differences and, as the implications from accepting partial residual invariance are still unknown (Putnick & Bornstein, 2016), we accepted noninvariance at the residual level. On the other hand, scalar invariance is a prerequisite for testing mean differences, because it reflects that the intercepts are not unequal across groups. Since this level of invariance was achieved, we were able to meaningfully compare mean scores of the PRF dimensions across mothers and fathers.

Parental Reflective Functioning in Mothers and Fathers
The main variables of pre-mentalizing, certainty about mental states, interest and curiosity, and infant socioemotional development were all significantly correlated. The independent samples t-test revealed differences across mothers and fathers on all three subscales. Mothers

Parental Reflective Functioning and Infant Socioemotional Development
The results from the multiple regression analyses for the effects of PRF on infant socioemotional development in first-time mothers and fathers are presented in Table 4. Higher levels of pre-mentalizing in mothers and fathers significantly predicted higher scores on the ASQ:SE-2, reflecting diminished socioemotional adjustment. Higher levels of certainty about mental states in mothers and fathers significantly predicted lower scores on the ASQ:SE-2, indicating improved socioemotional adjustment. No significant effects were found for interest and curiosity.

Discussion
We found that the PRFQ-I was a valid measure of PRF in first-time parents and that PRF, measured using PRFQ-I, had the same meaning across mothers and fathers. When comparing PRF dimensions in mothers and fathers, we found that mothers reported higher levels of certainty about mental states and interest and curiosity than fathers and that fathers reported higher levels of pre-mentalizing than mothers. Further, we found that pre-mentalizing and certainty about mental states measured at 4 months predicted infant socioemotional development at 11 months. Higher levels of pre-mentalizing predicted lower infant socioemotional adjustment, while higher levels of certainty about mental states predicted higher infant socioemotional adjustment. These results were seen in both mothers and fathers.
The first study aim was to test the factor structure and cross-gender measurement invariance of the PRFQ-I. We did this by examining the factor structure of PRFQ-I in a large community sample of first-time mothers and fathers of 4-month-old infants using confirmatory factor analyses. In line with Wendelboe et al. (2021), our results supported overall the PRFQ-I as a valid measurement instrument to assess the three PRF dimensions in mothers and fathers during the first year of parenthood.
With only three items in the PM subscale, Cronbach's alpha values for the subscale were low, and two of three items in the subscale showed low, yet significant, factor loadings, potentially reflecting low internal consistency. These findings are very similar to the previous study on the PRFQ-I (Wendelboe et al., 2021) and may be rooted in a mixture of methodological and theoretical explanations. A statistical explanation might be the low number of items in the PM subscale, since alpha values depend highly on the number of items in a scale (Cortina, 1993;Wendelboe et al., 2021). Similarly, the low factor loadings for two items in the PM subscale might be a result of low reliability of the three items (as indicated by the low alpha) and hence a heterogeneous subscale, where one item loads strongly on the latent variables while the other two have only weak loadings on the latent construct.
On a theoretical level, Wendelboe et al. (2021) suggested that a limited capacity for parental mentalization, captured by the PM dimension, might reflect three different modes of prementalizing: the psychic equivalence mode, the teleological mode and the pretend mode . The psychic equivalence mode represents a pre-mentalizing mode associated with disavowal of trying to mentalize others. As described previously, item 16 ("Often, my child's behavior is too confusing to bother figuring out") reflects this avoidance of mentalization and might tap into the psychic equivalence mode. The teleological mode reflects mentalization based on an extreme exterior focus . As such, item 1 ("The only time I'm certain my child loves me is when s/he is smiling at me") reflects this mode because a high score indicates a pre-mentalizing mode based primarily, and more or less exclusively, on the actual, observable behavior. Last, the pretend mode represents a pre-mentalizing mode that is somewhat detached from reality , with item 4 ("My child cries around strangers to embarrass me") reflecting this mode. Although these three pre-mentalizing modes generally reflect a limited capacity for parental mentalization, they capture different aspects of pre-mentalizing, which might partly explain the low internal consistency on the PM subscale. The CFA also revealed that item 11 on the CMS subscale, and items 15 and 18 in the IC subscale, had relatively low factor loadings. Item 15 states: "I try to understand the reasons why my child misbehaves." Parents of infants are probably less likely to use the word "misbehaving" to describe unacceptable or undesirable behaviour than parents of toddlers or older children. Item 11 ("I can sometimes misunderstand the reactions of my child") and item 18 ("I believe there is no point in trying to guess what my child feels"), being reverse coded, represent statements that parents of infants might be less likely to endorse than parents of older children. Hence, the low factor loadings on these items might be specific to parents of infants at 4 months.
Our results also indicated measurement invariance across parental gender at the configural, metric, and scalar level. Thus, our results imply that, in the present sample, PRF as a construct and the underlying items are equal across parental gender, for which reason differences in PRF dimensions as latent constructs for mothers and fathers can be validly interpreted. We did not find residual invariance, meaning that the residual variances were not equal across groups. Yet this level of invariance is the most restrictive because it reflects that the measurement error variances are equivalent across the examined groups (Putnick & Bornstein, 2016). However, since we obtained configural, metric and scalar invariance, we were able to validly compare the means of parental PRF between mothers and fathers in the current sample.
The second aim was to examine and compare mothers and fathers on the dimensions of PRF. Our results showed significant differences between mothers and fathers, with mothers reporting significantly higher levels of interest and curiosity and certainty about mental states than fathers, and fathers reporting significantly higher levels of prementalizing than mothers.
These results are partly in line with previous research showing significant differences on the dimensions of interest and curiosity and pre-mentalizing (Cooke et al., 2017;Gordo et al., 2020;Pazzagli et al., 2018;Salo et al., 2021). The findings could be explained by cultural and social norms resulting in mothers being the primary caregiver more often than fathers, and mothers taking more parental leave than fathers (Gordo et al., 2020;Salo et al., 2021). This was also the case in the present sample, in which the mothers had on average 9.9 months of maternal leave and the fathers had on average 2.35 months of paternal leave during the first 11 months of the child's life. Since mothers typically spend more time with their child in the first year of parenthood, this could potentially increase the level of interest and curiosity and decrease the level of pre-mentalizing because the higher amount of time alone with their child might give the mothers a greater opportunity for developing their mentalizing ability (Cooke et al., 2017). In line with this explanation, Cooke et al. (2017) found that the fathers in their study who spent more time with their children on weekends scored higher on interest and curiosity and lower on prementalizing than the fathers who spent less time with their children on weekends.
Unlike previous studies, we also found significant differences on the dimension of certainty about mental states, but the same explanation could be applied here as well. Mothers might be more certain of their infants' mental states because they spend more time with their child in the first 11 months after birth. However, although this finding was significant, the effect size for this difference was negligible compared with the effect sizes for the differences on the dimensions of interest and curiosity and pre-mentalizing.
Some studies found the differences on the dimensions of interest and curiosity and pre-mentalizing to persist in parents of older children, such as in parents of 12-month-old  and school-aged children (Pazzagli et al., 2018). Thus, it might be possible that the parental roles of mothers and fathers in early parenthood continue throughout parenthood, thereby affecting the dimensions of parental mentalization. However, Salo et al. (2021) did not find that these differences persisted 12 months postpartum, a finding that calls for further examination of the continuity or discontinuity of these gender differences during parenthood.
Our third aim was to examine the association between PRF at 4 months and infant socioemotional development at 11 months. We hypothesized that higher levels of prementalizing at 4 months were related to infant socioemotional development at 11 months. Confirming the hypotheses, and in line with previous research (Gordo et al., 2020;Nijssens et al., 2020), we found that higher levels of pre-mentalizing predicted diminished infant socioemotional adjustment. This was the case for both mothers and fathers. These findings show that high levels of pre-mentalizing negatively affect later infant socioemotional development, perhaps because parents with high levels of pre-mentalizing are at risk of making malevolent or distorted attributions regarding their child's mental states, which, in turn, might lead to reduced sensitivity in parental behavior affecting infant socioemotional development Gordo et al., 2020;Nijssens et al., 2020).
With regard to the two remaining dimensions of the PRFQ-I, certainty about mental states and interest and curiosity, we did not expect these to have an effect on infant socioemotional development, and, in line with previous research (Gordo et al., 2020;Nijssens et al., 2020), interest and curiosity did not significantly predict infant socioemotional development in mothers or fathers. However, our results showed that higher scores on the CMS subscale significantly predicted higher levels of infant socioemotional adjustment in both mothers and fathers. The positive effect of certainty about mental states on infant socioemotional development was not in line with the study by Nijssens et al. (2020). Notably, this study differed from the current study in a number of ways: the smaller sample size (n = 53), the different age of the sample (19-26 months) and the different measure of infant socioemotional development (BITSEA), which might all have contributed to the studies' contrasting results. The study by Gordo et al. (2020) used the same measure of infant socioemotional development as the present study; however, since they tested whether the effect of PRF on infant socioemotional development was mediated by parental competence, their results cannot be directly compared with those of the present study. In addition, the present study differs from the previous studies by examining the relation between PRF and infant socioemotional development longitudinally, while the studies by Nijssens et al. (2020) and Gordo et al. (2020) measured PRF and infant socioemotional development at one time point. Thus, these differences between the studies may have affected the contrasting results regarding the relation between certainty of mental states and infant socioemotional development. Nonetheless, the results from this study suggest a possible explanation for the effect of certainty about mental states on infant socioemotional developmentnamely, that a higher degree of certainty about mental states might help the parent to feel more competent in interpreting the infant's behavior, thereby allowing the parent to react more sensitively to the infant's socioemotional communication and underlying needs, and, by doing so, strengthen the infant's socioemotional development. Since only one previous study has tested parental competence as a mediator between PRF and infant socioemotional development, more mediational studies are needed to better understand the mechanisms underlying the association between PRF and infant socioemotional development.
On the other hand, research has shown that high scores on the CMS subscale might not be desirable. The CMS scale ranges from a parental tendency to feel complete lack of certainty to a tendency to be overly certain of the child's mental states . Hence, midrange scores might reflect the most optimal level of certainty about mental states, as we expect mentalizing parents to be able to know and interpret infant mental states to some degree, and at the same time to be able to recognize the opacity of mental states. In line with this, previous findings suggest that very high levels of certainty about mental states reflect hypermentalizing, which is a non-mentalizing stance in which the parent is overly certain of their child's mental states . Thus, too-high levels of this dimension might indicate intrusive mentalizing or even non-mentalizing, and not genuine mentalizing. In line with this interpretation, a midrange model for emotional non-verbal communication as being optimal has been confirmed in observational studies of mother-infant interaction by for example Tronick, Beebe and their colleagues. Tronick and Beeghly (2011) found that optimal dyadic exchange of emotion in mother-infant communication is characterized by ongoing disruptions and repairs, by messiness and not by perfect harmony. Likewise, Beebe and colleagues have confirmed that an optimum midrange model of mother-infant is optimal for child socioemotional development and secure attachment as opposed to interactions characterized by levels of co-ordination that are either too low or too high (Beebe et al., 2016). Low coordinated dyads are characterized by a form of withdrawal, disengagement or inhibition of relatedness, whereas dyads characterized by high coordination may be seen as being over-monitoring, indicating wariness or vigilance (Beebe et al., 2010). Future studies should determine whether high scores on the CMS subscale are associated with hypermentalizing as suggested by  or with more optimal development, as suggested by the results in the present study, and ideally also examine and define specific cutoffs for optimal scores on the other subscales of the PRFQ.
Although the present study has several strengths, including the longitudinal design and the large sample size, it also has limitations. First, although the sample was large, community based and included fathers, its representativeness might be questioned. The participating parents differed from the general Danish population in terms of educational level and ethnicity, and the sample did not include partners of other genders. Therefore, the generalizability of the results should be interpreted accordingly. Second, only parental self-report measures were applied in the present study, which raised the risk of bias such as measurement bias and social desirability bias. As the parents were the only informants in the study, their PRF might have affected how they evaluated their infants' socioemotional development. Future research should include multiple methods and informants to minimize bias.

Conclusion and Recommendations for Future Research
We found that the PRFQ-I was a good fit in a community sample of mothers and fathers 4 months postpartum and that the measurement instrument was invariant across mothers and fathers. This implies that PRFQ-I is a valid measure for examining PRF dimensions in early parenthood. However, the low alpha values and factor loadings related to the PM subscale point to the need for future studies examining the reliability and validity of this scale.
When comparing PRF dimensions in the mothers and fathers of infants, we found differences across all three dimensions of the PRFQ-I. Mothers scored higher on the dimensions of certainty about mental states and interest and curiosity, while fathers scored higher on prementalizing. This finding suggests that practitioners might benefit from having different points of attention when working with new mothers' and fathers' PRF. It also suggests that mothers and fathers might encounter different mentalization difficulties, for instance, fathers might be more prone to hypomentalize, whereas mothers might be more prone to hypermentalize.
Furthermore, we found that pre-mentalizing in mothers and fathers negatively impacted infant socioemotional development. This finding points to the need to identify mothers and fathers with high levels of pre-mentalizing to prevent potential negative effects on child development. To aid this identification, future studies should examine risk factors for high levels of parental pre-mentalization. Last, we found that higher levels of certainty about mental states in mothers and fathers promote infant socioemotional development. This finding has implications for health care professionals in contact with firsttime parents in early parenthood: Encouraging parents to reflect on their infant's mental states might enhance their ability to understand and interpret the mental states underlying the infant's behavior. In turn, this might increase parental competence and certainty about the child's mental states, thereby strengthening infant socioemotional development.
Thus, high levels of pre-mentalizing and low levels of certainty about mental states in fathers and mothers of infants could present intervention opportunities to support and enhance these specific aspects of PRF. On the other hand, identifying more optimal scores such as low levels of pre-mentalizing and moderate-to-high levels of certainty about mental states enables one to acknowledge and support the existing capabilities of parents of infants. Using a multidimensional approach such as the PRFQ-I as a screening tool and a preliminary assessment of PRF in applied settings could improve both the early identification of families in need of support in their parenting and the development of the existing competences of parents of infants. In Denmark, this could take place in the context of the national health-visiting program, in which a health visitor visits the family in the home several times during the first year of the child's life (e.g., Danielsdottir & Ingudottir, 2020).

Data Availability
The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request. Funding This work was supported by the Danish charity foundation Nordea-fonden. No grant number was provided.

Compliance with Ethical Standards
Conflict of Interest The authors declare no competing interests.
Ethical Approval This study was performed in line with the principles of the Declaration of Helsinki. Approval was granted by the Institutional Review Board at the Department of Psychology, with approval number IP-IRB / 23112018 (23/11-2018).
Consent to Participate Informed consent was obtained from all individual participants included in the study.
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