A bifactor model of U.S. parents’ attitudes regarding mediation for the digital age

ABSTRACT Parents use digital-specific strategies to mitigate online risks and augment online benefits of digital technology in their children’s lives. The goal of this study was to develop and validate a measure of parents’ attitudes about mediation of digital technology. An internet-based survey was administered to 460 parents of children and adolescents in the United States. Exploratory bifactor analysis revealed one general factor, reflecting general parenting attitudes, and four digital-specific factors: discursive mediation, restrictive mediation and monitoring, participatory mediation, and mediation by modeling. Confirmatory factor analysis supported a bifactor model of the Digital Parental Mediation Attitudes Scale (DPMAS); the general factor explained shared variance related to parenting style and skills in general, while the mediation factors represented digital-specific attitudes. Construct validity was evidenced in differential associations between mediation factors and parenting efficacy, influence, child age, and parent and child technology use patterns. Impact Summary Prior State of Knowledge: Research exploring the effectiveness of digital parenting strategies (e.g. discursive and restrictive mediation) has not conceptualized or measured these constructs consistently. This limits the extent to which scholars, policy makers, and parents can draw conclusions about the efficacy of digital parental mediation. Novel Contributions: To facilitate a coherent evidence base about digital parenting, the current study developed and validated a quantitative measure of US parents’ attitudes about mediation related to digital and social technologies using structural equation modeling. Practical Implications: The Digital Parenting Mediation Attitude Scale (DPMAS) assess parents’ attitudes across four dimensions (discursive, restrictive/monitoring, participatory, modeling) and can assist in the development and evaluation of interventions to support youth and families in a dynamic and rapidly evolving technological environment.

Mobile phone ownership in the US has grown rapidly (Anderson & Jiang, 2018), with 69% of 12-year-olds and 89% of 16-year-olds owning a smartphone (Rideout & Robb, 2019). While the current generation of children and adolescents were born into the technological era, their parents were raised in a less wired world. Sixty-six percent of parents feel parenting is harder today than it was 20 years ago, with 26% citing technology as the primary source of this difficulty (Auxier et al., 2020). Some parents do not feel they have knowledge or skills to effectively mediate digital technology, and that their children have comparatively higher digital literacy and skills (Krcmar & Cingel, 2016). The current generation of parents must attempt to guide children and youth through quickly evolving virtual contexts they themselves are learning to manage, and to use strategies that did not exist in their own childhoods to support and guide children's technology use. The term "parental mediation" originally referenced parents' roles (i.e. behavior) in regulating children's exposure to television. However, television and digital technologies have different affordances (boyd, 2010) and require unique parenting skills and strategies. Literature exploring what digital parenting skills and strategies are most effective and beneficial is expanding rapidly but has not been conceptualized or measured consistently. Scholars (e.g. Hefner et al., 2019;Livingstone & Helsper, 2008;Nikken & Jansz, 2014;Sonck, et al., 2013) have attempted to develop quantitative measures of digital mediation but results have not mapped onto hypothesized constructs cleanly. This lacuna limits the extent to which scholars, policy makers, and parents can draw overarching conclusions about the efficacy of digital parental mediation strategies. Previous efforts to measure this construct have focused upon parent-reported mediation behaviors; the current study builds upon this evidence base, but instead aims to develop and validate a quantitative measure of parents' attitudes about mediation related to digital and social technologies. Nathanson (1999) developed a theoretical model of parental mediation for television, with three dimensions: active mediation, restrictive mediation, and co-viewing (see also Jennings, 2017). This work was extended by Valkenburg, Krcmar, Peeters, and Marseille (1999), who developed a quantitative measure of television mediation. Active mediation involves teaching children about media and its content, can be protective against negative behaviors (e.g. aggression), and can facilitate development of critical thinking skills and moral reasoning (Clark, 2011). Restrictive mediation refers to establishment and implementation of rules and limits on content and duration of exposure. A balanced approach toward restrictive mediation results in better outcomes (Hefner et al., 2019;Katzet al., 2019). Although developmentally appropriate boundary setting is beneficial, too much restriction by parents can increase conflict and aggression and encourage alternate means of watching forbidden or limited content (Clark, 2011;Katz et al., 2019;Krcmar & Cingel, 2016). Co-viewing refers to passive (not discursive) parental presence while children are using media. This television-based framework (Nathanson, 1999;Valkenburg et al., 1999) has numerous failings when applied to digital technology; it does not address the bidirectional nature of online communication, the ubiquity of the technology outside of the home, or the increasingly solitary nature of digital media use (Jennings, 2017;Jiow et al., 2017;Sonck et al., 2013). Scholars (e.g. Jiow et al., 2017) have made efforts to update parental mediation theory to include additional dimensions like gatekeeping, discursive mediation, diversion, and investigative mediation.

Parental mediation theory and measurement
Using these theoretical models, researchers have applied quantitative strategies to explore the prevalence, dimensionality, and impact of parental mediation behavior related to digital technologies. Building upon the work of Valkenburg et al. (1999), Livingstone and Helsper (2008) asked British parents how often they utilized different mediation approaches. Their results suggested four types of mediation strategies: active co-use (items related to active mediation and co-use), interaction restrictions (limits on who children can interact with), technical restrictions (limits on content and time), and monitoring (checking of internet and email history). However, the strength and pattern of factor loadings were inconsistent, suggesting parental mediation behaviors in 2004 (when data were collected) had yet to coalesce around a set of digital-specific skills. Building on questions posed by Livingstone and Helsper (2008), Sonck et al. (2013) asked Dutch parents and their children questions about internet mediation across four subdimensions: active mediation, restrictive mediation, co-use, and monitoring. Results reflected a different pattern of factors than those of Livingstone and Helsper and co-use did not load cleanly onto a separate factor. Nikken and Jansz (2014) developed a measure of internet mediation behavior for parents of children ages 2-12. Like Sonck et al. (2013), factor analysis supported subdimensions of active and restrictive mediation. Different from Sonck et al., co-use emerged as a coherent factor, with two additional factors: supervision and technical safety guidance. Glatz, Crowe, and Buchanan (2018) examined internet-specific parental efficacy and internet-specific parenting practices. Adapting items used by Livingstone and Helsper (2008) and Sonck et al. (2013) across three dimensions (active mediation, restrictive mediation, and monitoring), Glatz and colleagues found monitoring and restrictive parenting practices loaded onto the same factor, supporting a two-factor solution.
The lack of consistency across studies in identifying coherent and consistent dimensions of digital parental mediation strategies suggests need for a more comprehensive effort to identify underlying dimensions of digital mediation behaviors. Prior studies have approached mediation from a behavioral perspective, asking parents to retroactively report on the frequency with which they engaged in mediational strategies. This approach introduces concerns about subjective recall and social desirability biases, as parent's subjective and retrospective reports are likely poorly indicators of their objective behavior. These concerns have been shown to be particularly relevant to technologyrelated behavior, like screen time (Ellis, 2019). Instead of this behavioral approach, the current study focuses on parents' attitudes and beliefs about digital mediation.

Contemporary digital parental mediation
Scholars have described aspects of digital parenting beyond those traditionally associated with mediation, including participatory mediation (Clark, 2011), investigatory mediation (Jiow et al., 2017), and modelling (Vaala & Bleakley, 2015). Participatory mediation parallels co-use, but also includes joint use of technological platforms to strengthen parentchild relationships, learn about the virtual activities and interactions in which children engage, monitor online social networks and interactions, learn about how technologies work, and learn about new technologies from children (Clark, 2011). As a result of shifts in parental norms to be more child-centered and less defined by hierarchical power structures participatory mediation is now a commonplace practice for parents (Clark, 2011) and is differentially associated with parent characteristics. Connell, Lauricella, and Wartella (2015) found that mothers engaged in less video game co-play than fathers, suggesting fathers may be more willing to engage in participatory strategies to learn about new games or applications. Older parents were less likely to co-engage, supporting findings that younger parents' higher technological confidence leads to more frequent participatory mediation. The more time parents spent on their own devices, the more likely they were to co-engage on video game platforms and tablets. In sum, the more comfortable and confident parents feel with technology, the more likely they are to engage in participatory strategies. This is a double bind for parents who feel less technologically capable, as they will be less likely to engage in participatory strategies to increase technological competence and self-efficacy.
The existing parental mediation literature has lacked attention to the knowledge and skills parents need to have to engage in mediation. Parents must have the necessary information and skills to know what to talk about when engaging in active mediation and co-use, and to set effective and developmentally appropriate boundaries (Jiow et al., 2017). Investigative mediation consists of "information seeking and skill acquisition" practices (p. 319) such as visually assessing digital content, seeking out information from other sources, playing video games or engaging on new social media platforms to better understand them, or asking others for help. Investigative mediation augments the effectiveness of other forms of parental mediation and helps parents differentiate strategies based on technology and child characteristics.
Parents employ modeling to help mitigate risks associated with digital technology (Hefner et al., 2019;Vaala & Bleakley, 2015). Many parents themselves are heavy users of digital and social technologies, and parent technology use is correlated with that of their children and adolescents (Vaala & Bleakley, 2015). Parents' problematic mobile phone involvement is a predictor of child problematic mobile phone involvement (Hefner et al., 2019). How parents utilize their devices and platforms sets an example for children and is an important aspect to be considered in the digital mediation toolkit.
Parents differentiate mediation strategies across childhood and adolescence. Nikken and Jansz (2014) found supervision was the most frequent form of mediation for young children, whereas restrictive mediation was more frequently employed with older children. Parents' application of restrictive parental mediation may be curvilinear, peaking in late childhood and early adolescence, when youth begin to use digital devices and platforms independently but have yet to develop the digital skills, autonomy, and selfregulation of older adolescents (Glatz et al., 2018;Sonck et al., 2013;Vaala & Bleakely, 2015). Active mediation likely also decreases as children enter adolescence (Padilla-Walker et al., 2012;Warren, 2017), potentially peaking in late childhood (Nikken & Jansz, 2014). Parents may differentiate mediation based upon concerns about online risks. Parents of younger children are more concerned with the impact of technology on cognition and development, whereas parents of older children are more concerned about the risks of cyberbullying and cybervictimization (Jeffery, 2020). Parents may feel less confident in their ability to effectively mediate as their children age, and thus engage in less mediation in general (Glatz et al., 2018;Livingstone & Helsper, 2008). Vaala and Bleakley (2015) suggested lower levels of mediation by parents of older adolescents may reflect adolescents' increasing individuation and less parental concern about rules and limits. Taken together, these findings underscore the centrality of developmental time to parents' mediation of digital technologies, but this has yet to be considered explicitly in parental mediation theory or measurement.

Digital parental mediation and general parenting style
Digital-specific parenting practices and general parenting are not independent, but rather synergistic and interrelated constructs. Parents likely utilize digital mediation skills and strategies consistent with their general parenting style and goal (Livingstone & Helsper, 2008). This supposition is supported by strong associations between general and digital-specific parenting constructs. Parents of young children who say they are doing a good job as parents are more confident in knowing how much screen time is appropriate (Auxier et al., 2020) and parents who feel more efficacious in general also experience more digital-specific parenting self-efficacy (Glatz et al., 2018). Parents who use more restrictive, active, and co-use mediation strategies across devices also report more general parental involvement and parentchild communication (Warren, 2017).
There are differences of magnitude and direction in how restrictive mediation, active mediation, monitoring, and co-use are associated with general parenting constructs. Hefner et al. (2019) found parents who reported higher parent-child attachment also reported engaging in more active mediation and monitoring, but not restrictive mediation. Also, those with secure parent-child attachments and more active/co-use mediation had children with less problematic mobile phone involvement (PMPI). However, parents who used the most restrictive mediation had children with higher PMPI, suggesting different directions of effects than found by Warren (2017). Vaala and Bleakley (2015) reported that adolescent-reported general parental monitoring was more strongly related to adolescents' internet behavior than internet tracking, internet restrictive practices, and co-use, suggesting monitoring in general is central to parents' influence on adolescents' digital lives and that internet tracking, restrictions, and co-use are not substitutes for general parental monitoring. Child disclosure is a large component of digital monitoring, suggesting close parent-child relationships are central to navigating the balance between minimizing online risks and maximizing benefits of digital technology (Jeffery, 2020;Vaala & Bleakley, 2015). Padilla-Walker et al. (2012) included general parenting constructs (maternal autonomy granting, connection, and regulation) as predictors of latent growth curves of restrictive mediation, active mediation, and deference (the choice not to intervene). Findings suggest that mothers high in autonomy granting may understand their adolescent's need for autonomy and grant their child more freedom over their media use at the start of adolescence and relax restrictions earlier than parents who are lower in autonomy granting style. Mothers who had strong relationships and engaged in frequent discussions with children were more likely to engage in digital mediation practices.
This poses a quandary for researchers of digital parental mediation: How to disentangle general and digital-specific parenting attitudes, strategies, and skills? Although we know these constructs operate synergistically, the development of an attitudinal measure of digital-specific mediation will facilitate the identification and evaluation of what attitudes and beliefs promote positive outcomes and mitigate risk within the digital aspect of parent-child relationships (Auxier et al., 2020). We hypothesized an attitudinal measure of digital mediation with a bifactor internal structure would best reflect this duality. Bifactor models have two components: a general factor that represents shared variance across all the items in the scale and group factors that represent additional shared variance among clusters of items (Reise, 2012). The general factor reflects a construct common to all the items in the scale, while the group factors represent separate constructs. We believe this structure is appropriate for an attitudinal measure of digital parental mediation, with the general factor representing covariance related to parenting style and the parent-child relationship in general, while the group factors represent covariance of digital-specific mediation dimensions.

The digital parental mediation attitudes scale
The purpose of this study was to develop and validate a measure of parents' attitudes about mediation strategies related to digital technology. We sought to test associations between digital mediation attitudes, pertinent demographic variables, and related parenting constructs to assess construct validity of digital-specific mediation dimensions. Based on existing theoretical and empirical work focusing on the conceptualization and measurement of digital parental mediation, we developed the Digital Parental Mediation Attitudes Scale (DPMAS). We initially hypothesized seven dimensions: discursive mediation, restrictive mediation, monitoring, co-use, modelling, investigatory mediation, and developmental appropriateness. These dimensions reflect both more traditional mediation theory (active and restrictive mediation, co-use) and more contemporary perspectives (modelling, investigatory mediation). In contrast to previous mediation scales, we designed the DPMAS to ask about attitudes towards mediation to reduce recall and social desirability bias and to focus on parental values, which are essential to gaining insight into parental practices (Darling & Steinberg, 1993).
Discursive mediation involves parental discussions with children about digital and social technology (Clark, 2011;Jiow et al., 2017). This dimension has also been termed active mediation (e.g. Nathanson, 1999), but the term discursive more accurately reflects that this dimension is about parent-child conversations. Restrictive mediation (Nathanson, 1999), also termed gatekeeping (Jiow et al., 2017), reflects use of age-and contextappropriate restrictions and boundaries on digital content, social connections, and time spent online. Monitoring reflects a technologized style of parental monitoring, defined as "a set of correlated parenting behaviors involving attention to and tracking of the child's whereabouts, activities, and adaptations" (Dishion & McMahon, 1998, p. 61). Co-use is when parent and child use digital technology together (Nathanson, 2015). Modelling reflects parents' recognition of their own digital behavior as a model for their children (Vaala & Bleakley, 2015). Investigatory mediation represents parents' choices to learn about and use about the technology and platforms their children use (Jiow et al., 2017). Developmental appropriateness represents parents' differentiated mediation strategies dependent upon the age of children (Jeffery, 2020;Padilla-Walker et al., 2012).

Domain identification and item generation
Seven hypothesized dimensions derived from the literature reviewed above served as the framework for a semi-structured, two-hour focus group with 12 mothers of children (aged early childhood through adolescence) in November 2019 (M age = 46), recruited through snowball sampling at a middle school. Focus group questions probed different ways in which parents engaged in parental mediation around the 7 core domains (see online supplement). Items for the DPMAS were generated based on focus group discussions; the first author utilized transcripts to identify terms and wording used by participants across the seven dimensions. Items were inspected by two expert reviewers (the second and third authors, psychologists with expertise in online and offline parenting) for content validity and clarity. After feedback was incorporated, 69 items were included in the survey.

Questionnaire evaluation
The 69 items were administered as part of an online survey, alongside a demographic questionnaire and scales to assess convergent and discriminant validity. Participants were recruited through CloudResearch, an online research platform that recruits participants from PrimePanels (Litman et al., 2017). Inclusion criteria were that participants had at least one child aged 5 to 18 at the time of the study (January 2020) and were living in the United States. The survey took 25 minutes to complete, and participants were financially compensated through CloudResearch. Institutional Review Board approved informed consent was obtained from all participants.
Participants who completed less than 80% of the survey (n = 10), who had no children (n = 3), and who took less than 588 seconds (i.e. time it would take to read all 12,000 characters in the online survey for a participant in the 95 th percentile of reading speed; n = 82) were removed from the sample, leaving 460 participants aged 20 to 69 (M = 40.67, SD = 7.20), 69.6% married with an average of 2.4 children with a mean age of 12.7 years (SD = 3.69). Participants identified as 61.1% cisgender female and 38.9% male (38.5% cisgender, 2 transgender), 75.2% White, 11.3% Black or African American, 7.8% Hispanic or Latino, 2.0% Asian, and 3.7% other. Participants had an average income in the $50,000-$69,000 range, and 60% had an associate's degree or higher (see online supplement; Table S1).

Digital parental mediation attitudes scale
Participants completed the 69-item Digital Parental Mediation Attitudes Scale (DPMAS). Parents rated the perceived importance of each item ("How important do you think it is to do the following with your child(ren) or adolescent(s)?") on a 5-point Likert scale (1-not important, 5-very important).

Perceived parenting self-efficacy and influence
Participants completed the 7-item efficacy subscale of the Parental Locus of Control Scale (Campis et al., 1986), which measures parents' global feelings of confidence with regard to parenting. Participants rated items on a 6-point Likert scale (1-disagree strongly, 6-agree strongly; ω = 0.77). Higher scores indicated that parents felt more effective in their parenting skills. Parents responded to the 5-item Perceived Influence Scale (Freedman-Doan et al., 1993), assessing the extent to which parents feel they can influence children's behavior with regard to school, peers, and externalizing behaviors. Participants rated how much influence they felt they had on a 7-point Likert scale (1-very little, 7-a great deal), with higher scores indicating greater perceived influence (ω = 0.89). Both constructs were modeled as latent variables (see online supplement).

Digital technology usage and experiences
Participants indicated the extent to which they and their children used various digital devices (desktop, laptop, smartphone, mobile phone, tablet, smartwatch, gaming console, kindle, other) which were summed as an index of the number of parent devices (M = 4.26, SD = 1.85) and number of child devices (M = 3.60, SD = 1.62). Participants indicated the extent to which they and their child(ren) used a variety of software application types (photo and video sharing, texting/messaging, gaming, reading and education, music and podcasts, entertainment

Parent and child characteristics
Parents reported their own age, gender identity, (0 = male, 1 = female), educational attainment (recoded as 0 = some college or less, 1 = college graduate or more), marital status (0 = not currently married, 1 = currently married), income (1 = less than $10,000per year to 7 = more than $150,000 per year), number of children in the family, and race/ ethnicity (recoded into two dummy variables representing self-identified Black and Hispanic race/ethnicities, with White and other racial/ethnic identities as the reference group).
Participants reported age and gender for up to six children. We felt that a mean-based approach to child age might mask parent's differentiation of mediation strategies by developmental stage. Instead, we modeled child age dichotomously (0 = all children in household are 13 years and younger, 1 = at least one child in the household is 14 years and older). Child/adolescent gender was coded into three categories: only female children, only male children, and both male and female children. This was operationalized by two dummy variables, one representing female-only families (1 = female only, 0 = all others) and another representing male-only families (1 = male only, 0 = all others), with mixedgender families as the reference group.

Analytic strategy
We used Stata/SE (version 17.0) to examine distributions of the DPMAS indicators; one DPMAS item ("Avoid texting and driving") fell outside the cutoff values (Bowen & Guo, 2011) for skewness (−0.286) and kurtosis (5.347) and was removed from analyses.
Focal analyses were conducted using structural equation modelling (SEM) in MPlus 8.6 (Muthén & Muthén, 1998 with MLR to account for non-normality and FIML for missing data. We evaluated model fit using best practices (Brown, 2015;Hu & Bentler, 1999). In addition to comparing nested models using chi-square difference tests (which are sensitive to sample size), we also utilized change in CFI ( � −0.01) as a marker of negligible difference between models (Cheung & Rensvold, 2002). We employed the Satorra and Bentler (2010) adjusted chi-square difference to calculate if the differences between nested models were significant.
The full sample (N = 460) was randomly separated into two subsamples for exploratory and confirmatory factor analyses. Exploratory bi-factor analyses (EBFA) were completed in subsample-A using a bi-geomin (oblique) rotation (Jennrich & Bentler, 2012;Reise, 2012). EBFA extracts all hypothesized subscale factors plus an additional general factor. In this instance, we hypothesized this general factor might represent general parenting skills and practices. Utilizing sub-sample B, confirmatory factor analyses (CFA) compared alternative model structures: a one-factor model, correlated-factors model, a second-order model, and a bifactor model (replicating the EBFA above with one general factor and digitalspecific factors). We completed measurement invariance testing of the final selected model across mothers and fathers in the full sample and analyzed internal consistency reliability of the bifactor model as specified by Hammer and Toland (2016). Finally, we estimated structural models to assess construct (convergent and discriminant) validity of the resultant DPMAS subscales. Specifically, we regressed the DPMAS subscales on demographic variables, indicators of technology usage and attitudes, and general parenting attitudes.

Exploratory bifactor analyses (EBFA)
The EBFA with sub-sample A indicated 10 factors with eigenvalues greater than 1, while parallel analysis and the scree plot suggested four factors. The RMSEA was lowest, and the CFI was highest, for the 7-factor solution with one general factor and six subscale factors (see online supplement; Table S2). The 7-factor solution had a significantly lower χ 2 value than the 8-factor solution, and the 8-factor solution was not significantly better than the 7-factor solution. However, closer examination of loadings in the 7-factor and 6-factor solutions revealed the 7 th and 6 th factors in these solutions had low factor determinacy, suggesting these factors represented measurement artifacts rather than viable solutions.
We thus decided to utilize the 5-factor solution, supported by equal RMSEA values and minimal Δ CFI in the 5-and 6-factor solutions. The 5-factor model made substantive sense; the hypothesized subscales (discursive mediation, restrictive mediation, monitoring, couse, education, developmental appropriateness, and modelling) collapsed into four theoretically coherent dimensions: (1) Fifteen Discursive Mediation (DM) items were originally included; eight loaded strongly onto the factor. Remaining items were dropped due to low communality (six items) and cross-loading onto two subscale factors (one item).
(2) Items from the hypothesized dimensions of restrictive mediation and monitoring loaded onto a single factor, termed henceforth Restrictive Mediation and Monitoring (RMM). Both hypothesized dimensions reflected rule-setting and rule-enforcing. Of the initial 18 items (11 restrictive monitoring, seven monitoring), six items from each of the restrictive and monitoring dimensions loaded significantly onto the restrictive mediation and monitoring factor. The other six items did not load significantly onto any subscale factor and were dropped. The dropped restrictive monitoring items referenced the use of technology to aid in holding boundaries (e.g. "Use technology to set limits on screen time"); given the relative novelty and diversity of these technologies, these questions may have been confusing or unclear to participants, resulting in poor fit. Two boundary-related items from the developmental appropriateness dimension loaded significantly onto restrictive mediation and monitoring ("Set time limits based on their age and maturity" and "Set content limits based on their age and maturity"). One hypothesized discursive item ("Discuss limits on content viewed online") loaded onto the restrictive mediation factor, resulting in a total of 15 items. (3) Items from the hypothesized co-use and investigatory mediation dimensions loaded onto a single factor, termed henceforth Participatory Mediation (PM). Both dimensions were intended to reflect parents' active engagement with technology as a form of connection and communication. All 10 original co-use items loaded onto this factor, as well as three parental education items. The other four parental education items did not load significantly onto any subscale factor and were dropped, resulting in a total of 13 items. (4) Nine (of 10) items from the originally hypothesized modelling dimension loaded significantly onto the Mediation by Modelling (MM) factor. One item ("Talk with your partner and/or family members about modelling appropriate digital behavior") did not load significantly onto any subscale factor and was dropped, leaving 9 items.

Confirmatory Factor Analyses (CFA) and measurement invariance
We used sub-sample B to examine how well these factors and items fit measurement models (i.e. CFAs) with different internal structures (one-factor model, correlated 4-factor model, second-order model, and bifactor model; see Table S3 in the online supplement). The bifactor model (i.e. a general factor and four subscale factors) had the best fit to the data. Analysis of the modification indices and residual variances indicated three items from the hypothesized developmental appropriateness dimension had poor fit; "Allow them more privacy as they grow in age and maturity" had high residual variance and "Set time limits based on their age and maturity" and "Set content limits based on their age and maturity" did not load significantly onto the restrictive mediation and monitoring (RMM) subscale. Modification indices and residual variances indicated the model would fit the data better if the uniqueness of items specific to social media (items 20, 21, and 22) and gaming (item 23 and 24) were correlated. With these respecifications (dropping three items and correlating the uniqueness of five items), all model fit indices suggested good fit for the bifactor model and fit well in the full sample (MPlus code is available in the supplemental materials). See Table 1 for the item wording and factor loading for each item from the full sample. Findings from the EBFA and CFA models suggest a significant portion of the variance among the digital-specific subfactors can be explained by a general factor, which may reflect that digital parenting attitudes are shared with parenting attitudes in general, but also have digital-specific unique variance. Examination of measurement invariance with respect to mothers (N = 280) and fathers (N = 180) revealed that the partial scalar invariance model did not significantly worsen model fit when compared to the metric invariance model (Δ χ 2 (41) = 43.633, p = 0.210 Δ CFI < 0.001). This suggests the DPMAS measures the same construct in both mothers and fathers and differences between these groups are because of different factor-level intercepts (means) and variances. A full explanation of these analyses and results (Table S4) can be found in the supplemental materials.

Dimensionality and internal consistency
Paralleling the theoretical development of the DPMAS, quantitative findings support the multidimensional bifactor structure of the measure. The DPMAS met all three signs that bifactor models are appropriate: subscale intercorrelation > 0.3, first-order factors loading onto second-order factor at > 0.5, and the ratio of the first to second eigenvalue is > 3 (Hammer & Toland, 2016). Intercorrelations of subscale factors were greater than 0.5 in the four-correlated factor model, first-order factor loadings were 0.650 in the second-order factor model, and the eigenvalue ratio was 5.74. The explained common variance (ECV) of the general factor was 0.558, less than the suggested 0.85 cutoff that would suggest the data would be best represented by a one-factor model (Stucky et al., 2014).
Results are presented fully in the online supplement (Table S5); the omega of the general factor (0.973), discursive mediation (0.896), restrictive mediation (0.952), participatory mediation (0.935), and modelling (0.933) were high. However, when we used the omega hierarchical to account for variance explained by the general factor, reliabilities of digital-specific dimensions were lower, with three falling below the 0.5 cutoff for independent use (Hammer & Toland, 2016). This finding is substantively coherent; we expected digital parenting skills and strategies to largely mirror parenting practices in general (i.e. for a general parenting factor to explain a large proportion of the variance) and for the remaining variance to reflect digital-specific attitudes. We thus recommend caution in utilizing the DPMAS subscales separately from the latent bifactor model or using a sum-score approach (McNeish & Wolf, 2020). Instead, we recommend using a latent variable bi-factor measurement model (in an SEM framework) to estimate optimal-weighting and variance/covariances of the general parenting factor and four subfactors (McNeish & Wolf, 2020). Within the structural model, digital-specific subfactors can then be specified in regression equations without the general parenting factor because it is still part of the overall model. Alternatively, factor scores for each of the sub-factors can be saved and used in subsequent analyses, although this approach is inferior at estimating error compared with a latent variable approach.

Construct validity of the DPMAS
To examine construct validity, we extended the bifactor measurement model to examine associations between the DPMAS subscales and relevant demographic and parenting variables and describe who was endorsing higher/lower levels on the DPMAS subscales. We regressed the DPMAS subscales onto demographic characteristics, technology usage and attitudes, and two general parenting scales. These structural models all had good fit to the data (RMSEA 0.040-0.048, SRMR 0.040-0.073, CFI 0.916-0.934) with results summarized in Table 2 and detailed in the online supplement. As expected, the DPMAS general factor and subscales were differentially associated with theoretically relevant independent variables in the model.

Discussion
Findings indicated the dual nature of parental digital mediation (reflecting both general parenting styles and digitally specific attitudes) is best represented in a bifactor model structure. The general parenting factor and digital mediation subscale scores were associated differentially, by both pattern and direction, with demographics, technologyrelated attitudes, and parenting efficacy, supporting construct validity of general and digitally specific mediation dimensions. Mothers scored higher on the general parenting factor (but not digital mediation subscales) than fathers, consistent with a literature suggesting mothers have greater availability and engage in more child caregiving overall than fathers (Connelly, 2015;Warren, 2017). Parents who reported higher conflict with children related to technology had higher levels of the general parenting factor, a pattern not found with any of the digital mediation factors. It could be that parents who do not place as much importance upon digital-specific mediation practices (and thus have more variance explained by the general parenting factor) have more conflict related to technology because they do not see these practices as necessary or important. Parents with higher tech-related confidence had significantly lower general parenting factor scores, suggesting parents who feel technologically confident are more apt to use digital-specific mediation practices, because they have the knowledge and skills to help children navigate activities and interactions in virtual contexts. The general parenting factor also had a different pattern of associations with general parenting attitudes (i.e. parenting efficacy and influence). Parents with higher global beliefs in their competence as parents had higher general parenting factor scores, supporting our assertion that this factor represents variance related to parenting in general. However, we did not find significant associations between parents' feelings of influence and general parenting factor scores, although influence was significantly associated with digital mediation factors. Taken together, these patterns suggest the general parenting factor represents a substantive source of general variance, while the subscale factors are more reflective of attitudes about digital-specific practices.
Parental endorsement of distinct DPMAS subscales varied based on several parental characteristics. As regressions were run in separate models, it is likely parents' education, income, and technology use each reflect socioeconomic status (SES) to some extent. Each of these predictors were significantly related to all four of the digital mediation factors. Higher SES parents likely have more fiscal resources and availability to engage in mediation behaviors.
The subscale discursive mediation represents discussions between parents and their children about digital technology. This subscale had the weakest loadings of the four, and individual items had the highest loadings onto the general factor, reflective of the overlap  between digital-specific discursive strategies and parenting in general. This is likely because most parents use discussion to support their children and mitigate risks across all facets of family life (Warren, 2017). Parents who feel they had more influence over children's behavior place more emphasis on discursive strategies (Krcmar & Cingel, 2016). Parents in this study who endorsed more digital-specific discursive strategies might have felt better able to guide children's behavior in general. This could be because discursive mediation strategies provide opportunities for parent involvement, parent-child communication, and parent connection (Padilla-Walker et al., 2012;Warren, 2017). We know parental mediation is but one component of the complex, bidirectional, and ongoing negotiations between parents and their children about technology (Jeffery, 2020), and it is therefore likely discursive strategies work both to exert influence and as a source of concern (through increased parental knowledge of online risks). Discursive strategies are likely a powerful tool for parents to develop open lines of communication about online experiences, exert influence, and gain information.
In contrast to Livingstone and Helsper (2008) and Sonck et al. (2013), but in keeping with Glatz et al. (2018), we did not find monitoring and restrictive mediation to be separate factors; items for both hypothesized dimensions loaded onto one factor. This makes sense, given the blurring of boundaries between these two constructs in the digital realm. Parents can now set and enforce limits using technology. Parents use rule setting, enforcement, and monitoring to mitigate children's exposure to risks (Clark, 2011;Jeffery, 2020). Parents' attitudes about restrictive mediation and monitoring were not associated with demographics, technology usage and attitudes, or general parenting attitudes in the same pattern as discursive mediation, participatory mediation, and mediation by modeling, suggesting this factor is tapping into a distinct dimension less aligned with positive parenting strategies. Parents with more children in their household were more likely to endorse restrictive mediation and monitoring practices, suggesting parents of larger families rely more on restrictive and monitoring practices, perhaps due to the higher total volume of their children's digital activity -or because they have learned more about restrictive and monitoring practices given their increased digital mediation experience across children. Restrictive mediation and monitoring was less endorsed as a strategy by parents of adolescents, consistent with previous findings that restrictive practices decrease during adolescence and is likely curvilinear, peaking in late childhood. Restrictive mediation and monitoring was also related to the numbers of hours parents reported they spent using digital technology. Parents who see themselves as heavier users of technology might not want the same for their children and thus use more restrictive strategies. Alternately, more intense users may have less time to engage in other types of mediation and rely more heavily on restrictive mediation and monitoring.
Participatory mediation assessed the degree to which parents believe in engaging with technology to connect with and learn from children. In our study, parents of adolescents placed greater importance on participatory mediation strategies than parents of younger children. This parallels findings of Rudi, Dworkin, Walker, and Doty (2015) and likely reflects patterns of more technological ownership and use by adolescents. Fathers were more likely to see participatory strategies as important, in line with previous research suggesting fathers may be more willing to engage in participatory mediation strategies to learn about new games or applications than mothers (Connelly, 2015). Parents who used screens more intensely themselves placed greater emphasis on participatory mediation, replicating findings of Connell et al. (2015) who found that the more time parents spent on their own devices, the more likely they were to co-engage on video game platforms. This may be because of both availability (the more parents use their own device, the more opportunities they have to connect with children digitally) and because these parents have increased comfort and skills with technology. This is a double bind for parents who have limited access to technology or high-speed internet, as they may feel less technologically capable and be less likely to engage in participatory strategies. Consistent with Krcmar and Cingel (2016), we found parents' feelings of influence were positively associated with participatory mediation, possibly because these strategies offer opportunities for parents to increase knowledge about child's digital activities/interactions and strengthen parent-child communication (Clark, 2011). However, our findings suggest participants with higher general parenting efficacy did not value participatory mediation strongly. As our study was cross-sectional, we cannot ascertain the directionality of this association; it could be parents who do not feel efficacious use participatory strategies to increase knowledge of children's behavior, opportunities for connection, and augment online influence/control. Alternately, it could be parents who feel globally efficacious do not feel it is necessary to engage in participatory mediation.
Mediation by modelling (MM) assessed the extent to which parents saw their own digital behavior as a tool in approaching digital mediation. Parents who strongly endorsed mediation by modelling items were more likely to have at least one adolescent in their household, perhaps because adolescents use digital technology more intensely than younger children and parents feel it is most important to model appropriate digital behavior to help them establish healthy habits. In addition, parents who reported higher efficacy placed less emphasis on modelling, but feelings of influence over child behavior were related to more importance placed on modelling.

Limitations and future directions
Parental mediation is not a unidirectional or static phenomenon (Jeffery, 2020). We collected data at a unique moment in time; we recruited US-based participants throughout January of 2020, only a few weeks prior to the COVID-19-related shutdowns. Parental attitudes about digital technology and mediation may be characterized by different priorities post-pandemic. In addition, our sample was comprised of a cohort of parents who did not grow up with digital technology. In the coming years, cohorts for whom social media and smartphones were part of their childhood and adolescence will themselves become parents; their styles of digital parental mediation will likely differ substantially from previous generations.
The study was completed using an online sample and our results may over-represent parents who feel more confident in their technological understanding, have higher incomes, or more positive attitudes towards technology. Within the US, children's use of digital technology and parents' mediation strategies vary by cultural context (Katz, 2017;Perrin, 2021); the current sample does not reflect this within-society heterogeneity and generalizability beyond the US-context is limited. Future longitudinal research with multiple informants and culturally specific sampling frames, as well as qualitative and within-group research designs, are necessary to elucidate the unique patterns of digital parental across cultural groups and global context. As our study design was cross-sectional, we were not able to identify causal relations between the DPMAS and other observed variables or understand these processes over time. Parental mediation consists of bidirectional interactions between parents and children, but we only collected data from parents. We could not ascertain the degree that parental and child viewpoints of mediation attitudes were congruent. Future studies should examine how children perceive their parents' mediation and how it correlates with parents' attitudes about digital mediation. Further, time constraints precluded a thorough assessment and analysis of potentially different parenting attitudes and practices towards individual children within the family, and measures rather referred to the child(ren) in the family more generally. This potentially obscured nuances within the family system. Future research should also utilize longitudinal designs with multiple informants, including all primary caregivers and children in the home, to gain the greatest insight into complex and dynamic family system across developmental time.
Our study also relied upon self-report measures that can bias results; this is especially true for retrospective questions about behavior. Previous studies (e.g. Hunt et al., 2018) have reported low correlations between objective and subjective measures of screen time. Future research should incorporate methods to assess these behavioral variables directly, possibly using screen shots of screen time applications or battery usage. Another limitation of the current study is the measurement of general parenting; we used only two dimensions of parenting (i.e. efficacy and influence). Future research should include additional dimensions of general parenting to further elucidate the relation between digital and general parenting.

Conclusion
The results of this study suggest that parental mediation of digital technology is a complex construct, not unlike parenting in general, and that there are digitalspecific mediation practices that parents use to help manage their children's digital media use and exposure. By incorporating an expansive approach to digital mediation (i.e. dimensions beyond active mediation, restrictive mediation, and co-use) and a bifactor structure, we hope that our four-dimensional measure (i.e. discursive mediation, restrictive mediation and monitoring, participatory mediation, and mediation by modeling) will be a valuable tool for future research and the development of educational interventions to support children, youth, and families in a dynamic and rapidly evolving technological environment.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Notes on contributors
Jessica L. Navarro is social worker and Assistant Professor in the department of Human Service Studies at Elon University. Her work explores the intersection of digital technology and family life, particularly parent-child relationships in the digital age. Dr. Navarro's research, practice, and teaching are grounded in bioecological theory.
Michaeline Jensen is a licensed psychologist and Assistant Professor of Psychology at the University of North Carolina Greensboro. She heads the Interactions and Relationships Lab, where her work leverages novel methodological techniques and mobile communication technologies to better understand the role of close relationships (e.g., with parents, peers) in the development of adolescent mental health and substance use.