Theoretical underpinnings of child-rearing practices

According to ^{Darling and Steinberg (1993}), parenting practices can be defined as goal-directed behaviors through which parents socialize their children. Research derived from the psychodynamic and social learning traditions (^{Darling & Steinberg, 1993}, for a review) and from the insights of ^{Baumrind (1967}, ¹⁹⁷¹, ¹⁹⁸⁹, ¹⁹⁹¹) and ^{Maccoby and Martin (1983}) have described parenting practices, in terms of two broad dimensions. Parental warmth or responsiveness reflects accepting, nurturing, supportive and responsive parenting behaviors that foster child’s individuality, self-regulation and self-assertion (^{Baumrind, 1991}; ^{Maccoby & Martin, 1983}). Parental control or demandingness can be understood as a set of parenting behaviors that involve maturity demands toward the child, the monitoring of child’s behaviors and the enactment of disciplinary actions, when needed (^{Baumrind, 1991}).

Several instruments have been designed to assess child-rearing practices in terms of parenting dimensions, with varying levels of specificity. Among them, the Child Rearing Practices Report (CRPR) has been widely used across children’s development (^{Dekovic et al., 1991}). Designed by ^{Block (1965}), the CRPR is a forced-choice Q-Sort rating system, consisting of 91 behaviorally anchored statements relevant to socialization that parents were asked to arrange on a seven-point scale (from the least to the most descriptive), with 13 prescribed items at each point. Although providing conceptually rich data on child-rearing, exploratory factorial analyses revealed that the number and internal consistency of dimensions derived from the CRPR Q-Sort varied from sample to sample (ranging from 21 to 33 factors) and represented highly-specific parenting qualities, such as independence, control, rationale guidance, enjoyment of child, expression of affection and punishment (e.g., ^{Block, 1980}; ^{McNally et al., 1991}; ^{Roberts et al., 1984}).

The Modified Child Rearing Practices Report Questionnaire (CRPR-Q)

To make the assessment less time-consuming and derive broader dimensions of parenting qualities, ^{Rickel and Biasatti (1982}) developed the Modified Child Rearing Practices Report Questionnaire (CRPR-Q). A questionnaire in the format of Block’s CRPR Q-Sort was administered to a sample of 211 undergraduate US students, many of whom were parents. A principal component analysis with varimax rotation led to the selection of a two-factor solution, composed of 40 items. On the one hand, the restrictiveness factor consists of 22 items that assess child-rearing practices that are characterized by a high degree of control toward children’s behaviors and feelings, the establishment of narrow limits on children’s behaviors, the endorsement of strict rules, requirements and restrictions. On the other hand, the nurturance factor includes 18 items that represents flexible child-rearing practices related to the willingness of parents to listen and share experiences with their children, as well as to demonstrate affection, acceptance and responsiveness toward their children’s needs. The internal consistency of both factors was corroborated in an independent sample of 95 parents, to whom the CRPR-Q was administered before attending parent training.

Since its development, the CRPR-Q has been used in a wide range of studies involving parents of preschool (e.g., ^{Andersson & Sommerfelt, 2001}; ^{Woolfson & Grant, 2006}) and/or school-aged children (e.g., ^{Andersson & Sommerfelt, 2001}; ^{Ceballo & Hurd, 2008}; ^{Lindhout et al., 2009}; ^{Root et al., 2016}) and adolescents (e.g., ^{Booth-LaForce et al., 2012}; ^{Murray et al., 2014}) and its two original factors have been accepted by most researchers. Nevertheless, the few studies that have investigated the factor structure of the CRPR-Q have failed to replicate the original two-factor solution proposed by ^{Rickel and Biasatti (1982}). ^{Dekovic et al. (1991}) examined the factor structure of the CRPR-Q in a sample of 239 Dutch parents (124 mothers, 115 fathers) of school-aged children, who had at least one child attending primary school who was nominated by peers as popular or rejected. The principal component analysis yielded a two-factor solution comprising 35 items. The confirmatory factor analysis showed that the model fit deviated significantly from the theoretical goodness of fix indices. Subsequent studies on the factorial structure of the CRPR-Q conducted in different cultural contexts (e.g., Indonesia, Brazil, Barbados Islands) have used principal component analysis procedures and yielded inconsistent findings concerning the number and content of identified factors, in samples of parents of preschool and school-aged children and adolescents (^{Chuang et al., 2013}; ^{Nunes et al., 2013}; ^{Payne & Furman, 1992}).

The highly contrasting findings in literature may reflect the use of principal component analyses procedures that capitalize on sample variability and highlight the need to explore further the factor structure of the CRPR-Q in community samples, using more advanced statistical tools. In fact, scholars have acknowledged that parenting practices can be described in terms of two main parenting dimensions that represent two theoretically independent goal-directed behaviors through which parents socialize their children (^{Darling & Steinberg, 1993}), but that these two parenting dimensions can be also considered together (^{Pinquart, 2017}) to understand the general emotional climate in which parents express these behaviors. Conventional factor analysis approaches may often fail to capture the multidimensionality of the latent structure of the CRPR-Q and more sophisticated modeling approach is needed. Bifactor models provide a flexible approach that allow to investigate multidimensional constructs that includes domain-specific dimensions that are expected to be independent and to determine whether an instrument has a general factor accounting for the commonality shared by these domain-specific dimensions (^{Morin et al., 2016}; ^{Reise, 2012}; ^{Reise et al., 2011}). This can contribute to a better understanding of the factor structure of the CRPR-Q. Furthermore, the assessment of conceptually-related constructs (such as, the two dimensions of parenting practices) and the fallible nature of indicators suggests that it is plausible to expect cross-loadings between items and non-target factors, so that it can be useful to rely on the exploratory structural modelling (ESEM) framework that integrates exploratory and confirmatory factor analyses (^{Morin et al., 2016}). The integration of bifactor modelling with ESEM (bi-factor exploratory structural equation modelling, B-ESEM) has been used to examine the issue of construct relevant multidimensionality and has demonstrated to be useful for scales refinement and validation, since it provides a comprehensive and flexible model to describe complex psychological constructs. However, to the best of our knowledge, the factor structure of the CRPR-Q has not been investigated previously using bifactor approaches.

Furthermore, prior research showed that parental reports of nurturance and restrictiveness did not differ, according to children’ sex (e.g., ^{Booth-LaForce et al., 2012}; ^{Murray et al., 2014}; ^{Payne & Furnham, 1992}). Although the parental perceptions of specific parenting qualities related to nurturance remain stable across children’s ages, extant studies showed an increase in parental reports of restrictiveness during early adolescence (^{McNally et al., 1991}; ^{Roberts et al., 1984}). However, the measurement invariance of the CRPR-Q across children’s sex (male vs. female) and age groups (children vs. adolescents) has not been previously examined.

To overcome the identified inconsistencies and gaps in the current state-of-the-art knowledge, the aims of the present study were (1) to investigate further the factor structure of the CRPR-Q, by using bifactor solutions (b-confirmatory factor analysis [B-CFA] and B-ESEM) obtained from two of the most conventional modeling approaches (CFA and ESEM) and (2) to examine the invariance of CRPR-Q across children’s sex and age groups (3-10 years vs. 11-15 years). Based on the literature, we hypothesized that the bifactor approaches would provide a more accurate representation of the distinct nature of the two dimensions (nurturance and restrictiveness) incorporated in the factorial model of the CRPR-Q. This approach also relies on a more precise disaggregation of the global construct supporting responses to all items (global factor) when compared with alternative models. With respect to measurement invariance, we expect that measurement invariance across children’s sex (male vs. female), but not across age groups (children vs. adolescents).

Participants

The participants were 589 mothers, recruited from Portuguese public schools in the Lisbon metropolitan area. The mothers’ ages ranged from 21 to 56 years old (M=39.36, SD=5.66). The majority of mothers were either married or cohabiting (70.2%). Children’s ages ranged from 3 to 15 years old (M=9.73, SD=3.67); 55.9% (n=329) were girls.

Measure

The Child Rearing Practices Report-Questionnaire (CRPR-Q, ^{Rickel & Biasatti, 1982}) is a 40-item self-report instrument that assesses parental child-rearing practices. From the original 40 items, four were dropped because their content related to sexual issues was perceived as inappropriate in several studies involving parents (e.g., ^{Nunes et al., 2013}). Parents were asked to focus on a specific child in the family to rate each item, using a 6-point Likert scale ranging from 1 (strongly disagree) to 6 (strongly agree). This measure comprises two subscales of 18 items each. Nurturance refers to parenting practices focusing on care, affection, and sharing feelings (e.g., “I express affection by hugging, kissing, and holding my child”). Restrictiveness is related to parenting practices focusing on control of the child’s behavior, according to values in which parents believe (e.g., “I prefer that my child not try things if there is a chance he will fail”). Item ratings pertaining to each subscale are averaged to yield a subscale score. Higher scores in each subscale indicate that parents perceive higher care, affection, and sharing of feelings (nurturance), or control of child behavior (restrictiveness), in their parenting practices. In the original study, the CRPR-Q showed good internal consistency (α =.84 for nurturance; .85 for restrictiveness) and validity (^{Rickel & Biasatti, 1982}). In our sample, Cronbach’s α was .83 for nurturance and .86 for restrictiveness.

Procedure

This study is part of wider research projects approved by the [Blind_for_Review] Ethics Committee. After obtaining the approval of the original authors, the CRPR-Q was translated into Portuguese, following a committee approach (^{Brislin, 1980}). After the translation of the CRPR-Q, the study was presented to the boards of participating schools to obtain the necessary authorizations for data collection. For children aged 3-10 years, school boards sent mothers an anonymous link to online informed consent and questionnaires by e-mail. For children aged 11 to 15 years, mothers were asked to complete an informed consent. After obtaining the mothers’ consent, teachers sent them the self-report questionnaire to be completed at home. After completion, the mothers returned the questionnaires to teachers in a closed envelope.

Data analysis

All missing data were excluded. From the original data set (626 participants), 37 observations were considered as multivariate outliers (p<.001) through the exploration of Mahalanobis distances; outliers were dropped from the study. The uni- and multivariate distribution of items was checked. Considering the absolute values of the univariate skewness (|Sk|>3) and kurtosis (|Ku|>7) (^{Kline, 2011}), two items had values indicating a violation of normal distribution. Item 2 (Sk[-3.92]; Ku[17.14]) had M=5.90 (SD=.36), with mode and median=6.00. Also, item 23 (Sk[-3.34]; Ku[13.97]) had M=5.82 (SD=.48), also with mode and median=6.00. Considering that the analyses were performed using the robust maximum likelihood (MLR) estimator method, these two items were not removed. None of the remaining items had values indicating the violation of the normal distribution (Sk[-2.41; .65]; Ku[-.93; 5.76]). The final sample consisted of 589 participants.

The two-factor structure of the CRPR-Q was estimated with four different solutions: an independent cluster model-confirmatory factor analysis (ICM-CFA), a bifactor model-confirmatory factor analysis (B-CFA), exploratory structural equation modeling (ESEM), and bifactor model-exploratory structural equation modeling (B-ESESM). All modeling analyses were conducted with Mplus 7.4 (^{Muthén & Muthén, 2012}). The robust maximum likelihood (MLR) estimator was used, since it provides standard errors and fit indices that are robust to the Likert-scale format of item responses and violations of normality (^{Morin et al., 2016}).

Model fit was assessed by examining the most common fit indices and information criteria: comparative fit index (CFI), Tucker-Lewis index (TLI), root mean square of approximation (RMSEA, with confidence intervals - CI), Akaike information criterion (CFI), Bayesian information criterion (BIC), and sample-size-adjusted BIC (ABIC). According to established standards (^{Hu & Bentler, 1999}), values closer or greater than 0.95 for CFI and TLI, and RMSEA values smaller than 0.06 were considered to be indicative of excellent model fit. Lower values of AIC, BIC, and ABIC were interpreted as reflecting a better fit to the data of one model in comparison to others with higher values. For testing alternative models, ΔCFI and ΔTLI≥0.01 and ΔRMSEA≥0.015 suggested more restrictive models, as argued by ^{Chen (2007}).

To clarify the factor structure of the CRPR-Q that best fits the data, the aforementioned contrasting models (ICM-CFA, B-CFA, ESEM, B-ESEM) were evaluated and compared (Figure 1).

Figure 1. Alternative structural models of CRPR-Q 

First, a CFA was conducted to test a two-factor solution, representing the two aforementioned correlated factors (nurturance and restrictiveness). This model was specified according to the ICM assumption, so that each item was allowed to load only on the factor it was assumed to measure, and all cross-loadings constrained to be zero. Second, a B-CFA model was tested, specified as orthogonal, so that all items were allowed to load simultaneously on one G factor and on their a priori S factors corresponding to the two distinct parenting practices, with no cross-loadings allowed between S factors. The orthogonal rotation ensured the interpretability of the solution in line with the bifactor assumption that the S factors reflect the part of item variance that is not explained by the G factor, whereas the G factor reflects the part of the item variance that is shared across all items (^{Morin et al., 2016}). Third, ESEM, which integrates CFA and EFA into a single structural equation model, was tested. This model was specified, using target rotation. Target rotation seems particularly appropriate, since it allows the pre-specification of target and non- target factor loadings in a confirmatory manner. Item loadings on their a priori factors and all cross-loadings were freely estimated, but “target” factor loadings were specified to be as close as possible to 0. Finally, the B-ESEM model was tested, using orthogonal target rotation. All items were allowed to define the G factor, while the two S factors were defined from the same pattern of target and non-target factor loadings and cross-loadings (similarly to the ESEM solution). Thereafter, analyses were conducted by using progressively more stringent invariance assumptions (^{Millsap, 2011}) to test measurement invariance across children’s sex and age groups.

Measurement invariance by children’s sex and age groups

Measurement invariance was tested across children’s sex (girls vs. boys) and age group (3-10 vs. 11-15 years) to investigate whether the best fitted model (B-ESEM) for the whole sample also fitted well for the aforementioned groups. Table 1 shows that an acceptable fit for sex was found. When the selected model was executed with the two sex groups nested, we did not observe a decrease in model fit larger than the recommended cut-off scores, suggesting configural invariance across sexes. Similar findings were observed when constraining factor loadings; factor loadings and intercepts; and factor loadings, intercepts, and uniqueness.

Table 1 shows that the two-factor B-ESEM solution was not invariant across children’s age groups. As displayed in Table 4, scores on nurturance were stable as children’s ages increased. However, scores on restrictiveness increased with children’s age.

Table 4 Means by nurturance and restrictiveness across age groups