Migration background and the measurement of home-based parental involvement in education: a psychometric evaluation of two self-report questionnaires

ABSTRACT

Home-based parental involvement in early education is linked to beneficial outcomes in children’s development and may redress unequal educational outcomes associated with family background. The type of educational activities at home and the way parents provide their support may differ across parents with and without a migration background. It is unclear whether home-based parental involvement is measured as the same construct across different origin groups. In this study, the psychometric properties of two parent-report questionnaires on home-based parental involvement were evaluated in 131 Dutch mothers of kindergarten-aged children, of whom 47% had a migration background. The dimensional structure of both questionnaires was tested with Principal Component Analysis. Multi-group confirmatory factor analyses were conducted to test for measurement invariance of the ‘Parenting Questionnaire’ across migration background. Results supported the multidimensional nature of home-based parental involvement, as formal and informal activities formed distinct components in the involvement of this diverse parent sample. In addition, measurement invariance was largely confirmed, indicating that parent’s involvement style can be validly measured across parents with and without a migration background in the Dutch context. Incorporating both formal and informal activities with involvement styles is recommended when measuring home-based parental involvement in different origin groups.

KEYWORDS:

• Migration background
• home-based parental involvement
• measurement invariance
• factor analysis
• parenting style

Introduction

Home-based parental involvement in children’s early education has been found associated with beneficial social, emotional, and cognitive outcomes in children’s development (Bakker et al. 2013; Carter 2002; Desforges and Abouchaar 2003). While the mechanisms underlying this link are not yet fully understood, previous studies have considered the potential of home-based parental involvement to redress unequal educational outcomes associated with children’s family backgrounds, such as immigration history (Cheadle 2008; St. Clair, Jackson, and Zweiback 2012). Studies on differences in home-based parental involvement and the association with child outcomes across parents with and without a migration background require instruments that assess the construct in an inclusive and equivalent manner across different origin groups. This study examined what home-based parental involvement in the Dutch kindergarten context may mean for parents with and without a migration background and how this meaning translates into the content and structure of two known questionnaires, covering multiple dimensions of home-based parental involvement.

The construct of home-based parental involvement

According to Bronfenbrenner (1977) and Vygotsky (Vygotsky, Rieber, and Hall 1998), the home environment of children is an important context for learning. Transactional models of development (Sameroff 1975) underlie the hypothesis that learning in home and school context do not proceed independently, but rather form a developmental cascade. Children who have, for example, experienced sensitive parenting are more likely to develop social and cognitive skills that in turn enhance the effect of formal schooling on their cognitive development (Guralnick 2017). Further, frequent exposure to high-quality shared book reading with a parent is associated with higher scores on reading and mathematics assessments (Barnes and Puccioni 2017). As such, parents can be viewed as children’s incipient teachers when involved in the child’s learning process, a role which continues to be of importance when children make the transition to school (Spruijt et al. 2018).

Home-based parental involvement in child learning has been defined as learning-related interactions that take place between children and parents outside of the school context (Hoover-Dempsey and Sandler 2005). Home-based parental involvement can include a wide variety of activities, both formal and informal. Formal activities can be defined as activities accompanied by direct instruction in specific skills and, when relevant, with a focus on printed letters and text, although definitions may slightly differ (compare LeFevre et al. 2009 with Sénéchal and LeFevre 2002). Informal activities can be defined as activities with an indirect educational component, like telling stories, singing, and cooking. Previous research has found a link between both formal and informal activities and children’s cognitive development (LeFevre et al. 2009; Sénéchal and LeFevre 2002; Skwarchuk, Sowinski, and LeFevre 2014). In addition to the formal and informal dimension, home-based parental involvement also differs in the climate parents create during their interactions with children, their home-based parental involvement style, or, in a broader context, parenting style (Jeynes 2007; Spera 2005). For example, autonomy support and management/discipline styles have been found positively associated with children’s learning and learning-related skills (Hindman and Morrison 2012; Matte-Gagné and Bernier 2011; Pomerantz, Moorman, and Litwack 2007). Different combinations of home-based parental involvement activities and styles, however, appear beneficial across ethnic groups (Day and Dotterer 2018; Lee and Bowen 2006). Studying these differences and differential effects of home-based parental involvement in families with and without a migration background is important as populations continue to become more diverse.

Migration, home-based parental involvement, and the Dutch context

Similar to other immigration countries, a sizeable proportion (24%) of the Dutch population has a migration background, meaning that either they or one or both of their parents were born outside the Netherlands (CBS 2020). Additionally, there is a ‘third generation’ that descends from one or more grandparents who were born abroad. While often not defined as a migrant generation, the migration background of their parents and grandparents may still have indirect effects through cultural heritage, social and cultural capital, societal stigma, and discrimination in schooling, housing, and labour market (de Vries 2016; Ypenburg 2009; Thijssen et al. 2019; Zorlu and van Gent 2020). In the Netherlands, the largest minority groups are from Turkey and Morocco, who initially were brought in for doing low-skilled work, and from Suriname and Indonesia, due to special relations stemming from the Dutch colonial history. The home-cultures of all four groups have been characterized as more collectivistic than the host culture (Hofstede 2002). Additionally, individuals with a migration background on average are lower educated, earn less than individuals from the Dutch majority and are more likely to be dependent on social benefits (CBS 2020; Den Ridder et al. 2020; Zorlu and van Gent 2020).

Due to these cultural and social-economic differences children with a migration background on average possess less cultural capital than children without a migration background (Lareau 2002; Lee and Bowen 2006). Migration background children may have to bridge differences in rules, expectations, speech patterns/dialect, views on appropriate behaviour or learning goals which can negatively impact their educational outcomes (Fleer and Hedegaard 2010; Hill and Torres 2010; Lareau 2002). In kindergarten, Dutch children with a migration background are out-performed by their non-migration background peers on cognitive and non-cognitive skills (i.e. a primary effect of migration background) (Zumbuehl and Dillingh 2020). Subsequently, even when controlling for parental education, children with a migration background were more likely to discontinue their educational career at an earlier stage than children without a migration background (i.e. a secondary effect of migration background) (de Winter-Koçak and Badou 2020). Home-based parental involvement might reduce unequal educational outcomes associated with immigration history as it can contribute to children’s cognitive development and may bolster academic persistence (Bakker et al. 2013; Cheadle 2008; Lareau 2001; Mena 2011; St. Clair, Jackson, and Zweiback 2012). As such, when migration background parents show high levels of home-based parental involvement this might compensate for the disadvantage of possessing less cultural capital (Lee and Bowen 2006).

Migration background and home-based parental involvement activities

Studies into home-based parental involvement and its effects mainly focused on formal activities, such as reading and helping with homework (Boonk et al. 2018). Studies on differences in home-based parental involvement between migration background and non-migration background groups have reported less formal involvement shown by parents with a migration background, such as in Germany (e.g. Klein, Biedinger, and Becker 2014; Niklas and Schneider 2013) and the US (e.g. Raikes et al. 2006). Also in the Netherlands, comparative studies have mainly focused on formal involvement. For example, parents with a migration background have been found to read less to their children than parents with a non-migration background (Kaufmann 2000; Leseman and van Tuijl 2013). Additionally, parents with a migration background have been found to provide less help with homework assignments compared to non-migration background parents (Rønning 2011). These differences, however, may be more a reflection of comparative studies’ focus on formal activities than of actual differences in the amount of involvement activities parents undertake (Leseman and van Tuijl 2013).

In Western host cultures (such as the Netherlands) parents value the early acquisition of literacy and numeracy skills in their children which activates formal involvement activities like reading and practicing numbers (Herweijer and Vogels 2013; Lareau 2002). In contrast, compared to non-migration background parents, parents with a migration background more often value transmitting their moral and religious values, and practices (i.e. non-dominant cultural capital), which does not necessarily require involvement in formal institutional teaching, but may activate informal involvement activities such as sharing oral stories or including children in everyday adult activities (Delgado-Gaitan 1992; Gallimore and Goldenberg 2001; Kaufmann 2000; Pels and De Haan 2007; Smit, Driessen, and Doesburg 2005). Parents with a migration background might therefore be more familiar with informal involvement activities in interaction with their children. As previously stated, such informal activities have also been found to support children’s cognitive development (e.g. LeFevre et al. 2009). Additionally, the transmission of non-dominant/ethnic cultural capital (such as religious norms and values) may contribute to the educational careers of children with a migration background (Shah, Dwyer, and Modood 2010).

Studies investigating how home-based parental involvement can reduce primary and secondary effects of migration background, therefore, need to capture the construct in an inclusive manner across different origin groups. To enable such studies, instruments should contain items that are relevant to all intended respondent groups (i.e. both formal and informal activities) and psychometric properties of these instruments should be investigated in a representative sample (Rattray and Jones 2007).

Migration background and home-based parental involvement style

Differences have also been found in home-based parental involvement styles across parents with and without a migration background. Parents with a Turkish and Moroccan background have been found less supportive of the child’s autonomy than native Dutch parents, which can co-occur with a less responsive instructional climate, more intrusiveness and more authoritarian forms of control (Huiberts et al. 2006; Pels, Distelbrink, and Postma 2009; Yaman et al. 2010). More examples can be found in international parenting research. For example, White American parents were rated by their children as more emotionally supportive than Asian American parents, who were seen as more demanding (Suizzo and Soon 2006). Differential impact of parental involvement style on child outcomes has also been found within and across countries (Pinquart and Kauser 2018). For example, in the US a parental involvement style characterized by strictness and control around schoolwork was associated with higher levels of educational attainment for African American children, but with lower grade point average and lower educational attainment for White children (Day and Dotterer 2018).

It is still unknown whether differences in involvement styles reflect true differences on the latent construct of home-based parental involvement style or subjective differences caused by interpretations of participants. In this context, it would be helpful to test whether the construct is measured the same across origin groups. Cultural conventions influence meaning ascribed to words and behaviour as well as perceptions of social desirability which can lead to differences in response styles across groups (Van de Vijver 2015). Additionally, items can also be interpreted differently due to limited language abilities. This could render the instruments used in comparative studies non-invariant and thus produce results that are unreliable (Putnick and Bornstein 2016). One way to examine this is to test whether an instrument’s factor structure is equivalent in different groups (Cheung and Rensvold 1998).

The present study

The current study evaluated the psychometric properties of two self-report questionnaires on parental home-based involvement administered in an ethnically diverse group of parents of preschool-aged children. Our research aims were twofold.

Firstly, we evaluated a home-based parental involvement questionnaire that measures the frequency of home-based parental involvement activities undertaken in families. As described in the Materials and Methods section, this questionnaire was expanded to include both formal and informal activities, with the aim of making the questionnaire more inclusive and relevant for both parents with and without a migration background in the Dutch kindergarten context. In our first set of analyses, we tested this assumption by exploring the internal factor structure of the adapted questionnaire in a combined group of parents with and without a migration background.

Secondly, the Parenting Questionnaire which assesses home-based parental involvement style was evaluated. Since this questionnaire was not adapted, and the internal structure was established in other studies (Hindman and Morrison 2012), we performed confirmatory factor analyses to test the previously found internal structure. Additionally, we tested this questionnaire for measurement invariance across parents with and without a migration background. To our knowledge, this study is the first to explicitly test the measurement invariance (MI) of a home-based parental involvement style questionnaire across parents with and without a migration background.

Materials and methods

Participants

The sample consisted of 131 mothers with a mean age of 36 (SD = 5.75) years. About half of the mothers reported a Dutch background (70 mothers, 53%), four (3%) reported a Turkish background, 13 (10%) Moroccan, 23 (18%) Suriname, and two (2%) reported a Dutch Antillean background. Furthermore, 19 (15%) chose the ‘other’ category. In the MI analyses, the 70 mothers who reported a Dutch background were compared to the 61 mothers that reported a non-Dutch background, who were considered as having a migration background. Most women (n = 102, 78%; 70 Dutch and 32 migration background) reported Dutch as their home language. Four (3%) women generally spoke Arabic, four (3%) another language, and 20 (15%) reported speaking a combination of Dutch and another language at home. One woman indicated she spoke another language than Dutch at home, but did not specify which language. A lower educational level was reported by 47% (highest completed degree either primary education, high school education, or the lower levels of tertiary education). This is less than 69% of the Dutch population of adults 15 years or older who are lower educated (CBS 2020). Of the Dutch parents, 19 mothers (27%) were lower educated and 51 (73%) were higher educated. In the group of mothers with a migration background, 42 mothers (69%) were lower educated and 19 (31%) were higher educated.

Procedure

Parents participated in a five-wave study on educational partnerships. School leaders of seven schools in the North-Western part of the Netherlands had agreed that parents and teachers from their school could be approached for the study. On average these schools hosted 243 pupils, ranging from 75 to 414 pupils. The seven schools varied in size, denomination (religious or not), ethnicity and social–economic status of their student population.

After gaining approval from the ethical committee of the Faculty of Behavioural and Movement Sciences from the Vrije Universiteit Amsterdam (VCWE-2015-140), recruitment started. Researchers, together with school leaders, organized a meeting at each school during which parents were informed about the study. Both parents were invited to participate. After participants provided their written consent they received the questionnaires via email, or if requested, in paper-and-pencil form. Participants who did not return their questionnaires within two weeks received a reminder via email. When parents did not respond to a first reminder, they received a second email after another two weeks. After two reminders by the researcher, teachers provided one last reminder via email or face-to-face. In schools with low return rates parents were given the opportunity to fill in the questionnaire on paper. One school followed a different approach. The school leader requested that parents would be invited to fill in the questionnaires on paper in the waiting area when they came to school for their regular parent-teacher meetings. Questionnaires were used to collect demographic data and assess home-based parental involvement activities and styles. All questionnaires were in Dutch. When needed, parents who had insufficient command of the Dutch language were assisted by an interpreter. One parent was provided with a translated version of the questionnaire. Data from the first measurement wave were used in the current study

Measures

Home-based parental involvement activities

A previously used questionnaire with satisfactory internal consistency is the Parental Involvement Questionnaire (Walker et al. 2005). This instrument allows for the involvement of all members of the nuclear family to be reported which makes the instrument more culturally inclusive and less sensitive for background variables such as parents’ working hours. The original scale consisted of 10 items divided over two sub-scales: Home-based Involvement and School-based Involvement, with 5 items each. For this study, the questionnaire was translated to Dutch by a native English speaker. To check the quality of the translation another researcher translated the items back to English. Any inconsistencies were discussed until a satisfactory translation was reached. Four items from the School-based Involvement sub-scale were not included as our focus was on involvement in the family environment. Concerning the Home-based Involvement subscale, the item ‘Someone in this family helps this child study for tests’ was also omitted as it was considered unsuitable for the kindergarten context. Two other items were slightly adapted to be more applicable for this context. ‘Someone in this family supervises this child’s homework’ was adapted to ‘Someone in this family supervises this child’s work for school’. ‘Someone in this family practices spelling, math, or other skills with this child’ was adapted to ‘Someone in this family practices words, numbers, or concepts with this child’. The resulting five items represent formal activities that parents can undertake to support their children’s development (see Table 1).

Table 1. Items and their Endorsement Frequencies Quantitative Home-based Involvement Questionnaire.

		Answer categories
	Items	Never	Less than once a month	Once a month	Once a week	Multiple times a week	Every day	Missing
Original	1. Talks with this child about the school day.	1 (.8%)	–	1 (.8%)	–	17 (13%)	112 (85.5%)	–
Original/adapted	2. Supervises this child’s work for school.	16 (12.2%)	3 (2.3%)	4 (3.1%)	17 (13%)	59 (45.4%)	31 (23.7%)	1 (.8%)
Original/adapted	3. Practices words, numbers, or concepts with this child.	3 (2.3%)	–	1 (.8%)	21 (16%)	72 (55.4%)	33 (25.2%)	1 (.8%)
New	4. Reads to this child.	–	1 (.8%)	3 (2.3%)	9 (6.9%)	41 (31.1%)	77 (58.8%)	–
New	5. Sings with this child.	5 (3.8%)	2 (1.5%)	1 (.8%)	17 (13%)	52 (39.7%)	54 (41.2%)	–
New	6. Plays with this child.	–	1 (.8%)	1 (.8%)	5 (3.8%)	47 (35.9%)	76 (58%)	1 (.8%)
Original	7. Reads with this child.	14 (10.7%)	4 (3.1%)	2 (1.5%)	17 (13%)	44 (33.6%)	48 (36.6%)	2 (1.5%)
New	8. Tells stories to this child.	1 (.8%)	4 (3.1%)	3 (2.3%)	13 (9.9%)	53 (40.5%)	56 (42.7%)	1 (.8%)
New	9. Jokes with this child.	–	–	2 (1.5%)	1 (.8%)	33 (25.2%)	93 (71%)	2 (1.5%)
New	10. Goes to the library with this child.	43 (32.8%)	25 (19.1%)	40 (30.5%)	13 (9.9%)	5 (3.8%)	5 (3.8%)	–
Original/dif. subscale	11. Helps out at this child’s school.	21 (16%)	50 (38.2%)	26 (19.8%)	7 (5.3%)	10 (7.6%)	15 (11.5%)	2 (1.5%)

Subsequently, we added six items addressing informal daily activities to make the instrument more inclusive. Item development was done by a group of six experts in the field of parenting, parental involvement, and parenting practices of parents with a migration background. A sample item is ‘Someone in this family tells stories to this child’. Like the original items from the Home-based involvement scale, these items were administered on a 6-point scale (1 = never 2 = less than once a month, 3 = once a month, 4 = once a week, 5 = multiple times a week, and 6 = every day). The questionnaire was renamed Quantitative Home-based Involvement Questionnaire. An overview of the items and their endorsement frequencies is given in Table 1.

Home-based parental involvement style

Home-based parental involvement style was assessed with the Parenting Questionnaire (Hindman and Morrison 2012). This instrument includes 17 items, divided over three subscales: Home Learning Environment (HLE), Autonomy Support / Expectations (AUT), and Management / Discipline (MD). The original English version consisted of 14 qualitative and three quantitative items. For this study, the three quantitative items were omitted, because similar items were part of the Quantitative Home-based Involvement Questionnaire. Furthermore, the item ‘I encourage my child to do math-related activities’ was adapted to suit the kindergarten context and reworded as ‘I encourage my child to do calculus’ because the Dutch word for mathematics is not used until high school. A sample item is ‘I encourage my child to write’. Items were administered on a 5-point scale (1 = not at all like me to 5 = very much like me). For the items of the subscales HLE and MD the categories ‘not at all like me’ and ‘not like me’ were rarely endorsed in this sample, and therefore collapsed into one, hence analysing four instead of five categories for these subscales. The spread of endorsement frequencies was different for items of the subscale AUT. For these items, we combined the categories ‘not at all like me’, ‘not like me’, and ‘somewhat like me’. ‘Like me’ and ‘very much like me’ remained separate categories. As a result, for the AUT subscale, three instead of five categories were used in the analyses. An overview of the items and their original endorsement frequencies is given in Table 6.

Strategy of analysis

First, correlations among the items of each questionnaire were computed and assessed (Cohen 1988) and the internal consistency was assessed by computing Cronbach’s alpha. Cronbach’s alpha reflects the internal consistency of the items and is an indication of the reliability of the questionnaire. A higher Cronbach’s alpha means a more reliable questionnaire. Criteria for internal consistency are taken from Ponterotto and Ruckdeschel (2007). Second, to explore the factor structure of the Quantitative Home-based Involvement Questionnaire we performed a Principal Component Analysis (PCA) in IBM SPSS Statistics version 24. We chose the exploratory PCA approach because the factor structure of the Quantitative Home-based Involvement Questionnaire, consisting of both existing and newly developed items, is unknown (Fokkema and Greiff 2017; Ziegler 2014). A rotated oblimin PCA, allowing for correlated components, was run. Components were selected on the basis of an eigenvalue larger than 1.00 and the scree plot was inspected (Cattell 1966; Kaiser 1958). Subsequently, the interpretability of components was assessed by examining the factor loadings, which represent the strength of the relationship of the item with that component. The rotated components should contain items with factor loadings larger than .35 that do not load highly on another dimension (i.e. the item clearly is most important for one particular component) and items loading on a component should share the same conceptual meanings.

With regard to the Parenting Questionnaire, the proposed three-factor structure (Hindman and Morrison 2012) was tested using confirmatory factor analysis in Mplus Version 7.31 (Muthén and Muthén 2015). Multi-group confirmatory factor analysis (MCFA) for categorical data with weighted least squares mean and variance adjusted (WLSMV) as an estimator was performed to test different levels of MI with respect to migration background (Gooden and Li 2016; Milfont and Fischer 2010; Vandenberg and Lance 2000). In the first step, we tested for configural invariance, meaning that the three-factor structure holds across both groups. This is the least constrained model of invariance where the fitted factor model is the same, but the parameter estimates (i.e. item thresholds, residual item variances, and factor loadings) may differ across groups. Item threshold reflects the ‘difficulty’ of the item: the higher the threshold, the lower the probability of answering one of the higher categories of the item. Factor loadings represent the strength of the relationship of the item with that factor. The higher the factor loadings, the stronger the item is related to the factor, hence, the better it is as an indicator of the construct the questionnaire intends to measure. Residual item variances reflect the amount of item-specific variance that is unrelated to the latent construct (and includes measurement error in the item). In the second step, we tested for metric invariance. In this model, in addition to assuming the same factor structure in both groups of parents, the factor loadings are constrained to be equal across groups. If this model fits well, metric invariance holds. This implies that the strength of the association between the factors and the items is the same across groups. In the third step, we tested for scalar invariance by further constraining the model by setting the item thresholds to be equivalent in the two groups. If support for scalar invariance is found, this means that the endorsement of a specific item on the questionnaire by parents reflects the same underlying latent response that is irrespective of group membership. Hence, factor means can be meaningfully compared across groups. In the last step, strict factorial invariance was tested by additionally constraining the residual item variances to be equal across groups. If strict factorial invariance holds, this means one can assume that differences in item scores between the groups reflect true differences in the construct.

The fit of each model was evaluated by the adjusted chi-square test, Root Mean Square Error of Approximation (RMSEA), Comparative Fit Index (CFI) and Tucker-Lewis Index (TLI) adhering to guidelines for models with categorical data (Van de Schoot, Lugtig, and Hox 2012; Yu 2002). In addition, model fit was compared between subsequent models, that is, each more constrained model was compared to the model tested in the previous step (Milfont and Fischer 2010; Putnick and Bornstein 2016). If the model fit of the more constrained model (e.g. the metric invariance model, with factor loadings constrained to be equal across groups) was not significantly worse than the fit of the less constrained model (e.g. the configural invariance model), support for the more stringent level of MI is found. The difference in model fit was evaluated with the adjusted chi-square difference test and the change in RMSEA and CFI (Chen 2007).

Results

Item frequencies and correlations of the quantitative home-based involvement questionnaire

Prior to exploring the factor structure of the Quantitative Home-based Involvement Questionnaire, we inspected the item endorsement frequencies (Table 1) and the inter-item correlations (Table 2). A preliminary examination of the bivariate correlations amongst the items of the Quantitative Home-based Involvement Questionnaire revealed that 26 out of 55 inter-item correlations were statistically significant, ranging from .18 to .51. Of the significant correlations, one was of large effect size, nine were medium, and 16 were weak. All items, except the first, correlated significantly with at least one other item. The Cronbach’s alpha for the complete Quantitative Home-based Involvement Questionnaire was .64 (unsatisfactory).

Table 2. Inter-Item correlations Quantitative Home-based Involvement Questionnaire.

	2	3	4	5	6	7	8	9	10	11
1. Talks with this child about the school day.	.13	.13	.06	.04	.13	.12	.15	.12	−.05	.07
2. Supervises this child’s work for school.	–	.33**	−.03	.01	.05	.16	.30**	.11	.24**	.29**
3. Practices words, numbers, or concepts with this child.	–	–	.12	.14	.13	.19*	.32**	.21*	.05	.31**
4. Reads to this child.	–	–	–	.13	.20*	.21*	.25**	.25**	.18*	.00
5. Sings with this child.	–	–	–	–	.42**	.16	.20*	.25**	.07	.16
6. Plays with this child.	–	–	–	–	–	.23*	.36**	.51**	.06	.05
7. Reads with this child.	–	–	–	–	–	–	.49**	.08	.19*	.18*
8. Tells stories to this child.	–	–	–	–	–	–	–	.41**	.19*	.23**
9. Jokes with this child.	–	–	–	–	–	–	–	–	.09	.06
10. Goes to the library with this child.	–	–	–	–	–	–	–	–	–	.38**
11. Helps out at this child’s school.	–	–	–	–	–	–	–	–	–	–

*. Correlation is significant at the 0.05 level (2-tailed).

**. Correlation is significant at the 0.01 level (2-tailed).

Exploring the factor structure of the quantitative home-based involvement questionnaire

The PCA for the Quantitative Home-based Involvement Questionnaire revealed that the 11 items could be reduced to four components (with eigenvalues larger than 1: 2.69, 1.75, 1.24, and 1.03, together explaining 61% of the variance). Individually the four components explained 24%, 16%, 11%, and 9% of the variance, respectively. The scree plot did not show a clear point where the slope of the curve clearly levelled off. We therefore first explored the rotated solution of the four-factor solution, see Table 3.

Table 3. Standardized Component Loadings of the rotated 4-factor solution Quantitative Home-based Involvement Questionnaire.

Item	Component 1	Component 2	Component 3	Component 4
1. Talks with this child about the school day.	.00	.19	.70	.17
2. Supervises this child’s work for school.	.01	.79	−.07	−.08
3. Practices words, numbers, or concepts with this child.	.08	.66	.14	.04
4. Reads to this child.	.14	−.36	−.10	.77
5. Sings with this child.	.72	.08	−.14	−.14
6. Plays with this child.	.81	−.05	.07	.19
7. Reads with this child.	−.21	.31	.02	.62
8. Tells stories to this child.	.43	.25	.05	.54
9. Jokes with this child.	.76	−.00	.07	−.02
10. Goes to the library with this child.	.03	.12	−.73	.30
11. Helps out at this child’s school.	−.00	.52	−.54	.08

Note. Eigenvalues of the components were 2.69, 1.75, 1.24, and 1.03, respectively.

The pattern matrix revealed two components that should clearly be retained according to the interpretability criteria. Component 1 contained three items, reflecting informal activities. Component 4 included three items reflecting language/literacy activities. Component 2 contained only two items with the highest loading on that component, reflecting formal, school-related activities. Component 3 contained three items with distinctly different conceptual meanings. The item ‘Helping out at the child’s school’ also loaded positively and above .3 on Component 2 to which it also showed a better conceptual fit. As such, we decided to force a three-factor solution. When a three-factor solution was forced, the pattern matrix gave two components that should clearly be retained according to the interpretability criteria, see Table 4. Component 1 contained five items reflecting informal involvement activities. Component 2 included four items reflecting formal, school-related involvement activities. The language/literacy items were redistributed across these two components in predictable ways. Component 3 contained two items that did not share the same conceptual meaning. The item ‘Going to the library’ also loaded positively and above .3 on Component 2 to which it also showed a better conceptual fit. This suggested a two-factor solution might be more clear and parsimonious than the four- and three-factor solutions.

Table 4. Standardized Component Loadings of the rotated 3-factor solution Quantitative Home-based Involvement Questionnaire.

Item	Component 1	Component 2	Component 3
1. Talks with this child about the school day.	.06	.26	.68
2. Supervises this child’s work for school.	.−.11	.73	−.02
3. Practices words, numbers, or concepts with this child.	.03	.66	.17
4. Reads to this child.	.51	−.04	−.20
5. Sings with this child.	.62	−.03	−.06
6. Plays with this child.	.86	−.03	.11
7. Reads with this child.	.04	.57	−.05
8. Tells stories to this child.	.62	.43	.03
9. Jokes with this child.	.72	−.07	.12
10. Goes to the library with this child.	.14	.23	−.75
11. Helps out at this child’s school.	−.03	.54	−.52

Note. Eigenvalues of the components were 2.69, 1.75, and 1.24, respectively.

The two-factor solution produced components with eigenvalues of 2.69 and 1.75 (explaining 40% of the variance), see Table 5. This solution produced only one cross-loading above .30 and no negative loadings. Item 1 (Talks with this child about the school day) had a factor loading below .30 on either component and was dropped. Component 1 encompassed five items that refer to informal activities and could be labelled ‘Learning through play’. Component 2 consisted of the other five items and could be labelled ‘Support of Learning’. There was a small correlation between the two components (r = .08). These results suggest a two-factor solution with separate scales for ‘Learning through play’-items and ‘Support of Learning’-items fitted the data best. Internal consistency for the two subscales was α = .70 (moderate) and α = .56 (unsatisfactory), respectively.

Table 5. Standardized Component Loadings of the rotated 2-factor solution Quantitative Home-based Involvement Questionnaire.

Item	Component 1	Component 2
1. Talks with this child about the school day.	.13	−.12
2. Supervises this child’s work for school.	−.08	.66
3. Practices words, numbers, or concepts with this child.	.07	.50
4. Reads to this child.	.49	.10
5. Sings with this child.	.61	.04
6. Plays with this child.	.86	−.03
7. Reads with this child.	.06	.54
8. Tells stories to this child.	.63	.40
9. Jokes with this child.	.72	−.08
10. Goes to the library with this child.	.09	.60
11. Helps out at this child’s school.	−.04	.75

Note. Eigenvalues of the components were 2.69 and 1.75, respectively.

Item frequencies and correlations of the parenting questionnaire

Prior to testing the factor structure of the Parenting Questionnaire, we inspected the item endorsement frequencies in both groups (with and without a migration background). An overview of the items and their original endorsement frequencies is given in Table 6.

Table 6. Items and their Endorsement Frequencies Parenting Questionnaire of Parents with and without a Migration Background.

Factor	Item descriptions	Not at all like me	Not like me	Somewhat like me	Like me	Very much like me	Missing
HLE	1. Encourage to write	NM: 1 (1.4%) M: 2 (3.3%)	NM:6 (8.6%) M: 6 (9.8%)	NM: 16 (22.9%) M: 15 (24.6%)	NM: 26 (37.1%) M: 18 (29.5%)	NM: 21 (30%) M: 20 (32.8%)	NM: - M: -
HLE	2. Encourage to do calculus	NM: 7 (10%) M: 1 (1.6%)	NM: 6 (8.6%) M: 5 (8.2%)	NM: 19 (27.1%) M: 15 (24.6%)	NM: 20 (28.6%) M: 26 (42.6%)	NM: 17 (24.3%) M: 14 (23%)	NM: 1 (1.4%) M: -
HLE	3. Provide workbooks	NM: 20 (28.6%) M: 5 (8.2%)	NM: 10 (14.3%) M: 7 (11.5%)	NM: 21 (30%) M: 19 (31.1%)	NM: 14 (20%) M: 20 (32.8%)	NM: 4 (5.7%) M: 10 (16.4%)	NM: 1 (1.4%) M: -
HLE	4. Play number games	NM: 4 (5.7%) M: -	NM: 5 (7.1%) M: 6 (9.8%)	NM: 14 (20%) M: 10 (16.4%)	NM: 31 (44.3%) M: 27 (44.3%)	NM: 15 (21.4%) M: 18 (29.5)	NM: 1 (1.4%) M: -
AUT	5. Respect child’s opinion	NM: - M: -	NM: 1 (1.4%) M: 2 (3.3%)	NM: 5 (7.1%) M: (%)	NM: 27 (38.6%) M: 22 (36.1%)	NM: 37 (52.9%) M: 32 (52.5%)	NM: - M: -
AUT	6. Encourage exploration	NM: - M: -	NM: - M: 1 (1.6%)	NM: 7 (10%) M: 7 (11.5%)	NM: 19 (27.1%) M: 28 (45.9%)	NM: 44 (62.9%) M: 25 (41%)	NM: - M: -
AUT	7. Encourage child to talk	NM: - M: -	NM: - M: 2 (3.3%)	NM: 3 (4.3%) M: 2 (4.9%)	NM: 20 (28.6%) M: 24 (39.3%)	NM: 47 (67.1%) M: 32 (52.5%)	NM: - M: -
AUT	8. Considerate of others	NM: - M: -	NM: - M: -	NM: 3 (4.3%) M: 1 (1.6%)	NM: 18 (25.7%) M: 24 (39.3%)	NM: 49 (70%) M: 35 (57.4%)	NM: - M: 1 (1.6%)
AUT	9. Spend time with child	NM: - M: -	NM: - M: -	NM: 1 (1.4%) M: 2 (3.3%)	NM: 16 (22.9%) M: 21 (34.4%)	NM: 53 (75.7%) M: 38 (62.3%)	NM: - M: -
AUT	10. Child to be responsible	NM: - M: -	NM: 1 (1.4%) M: -	NM: 2 (2.9%) M: 6 (9.8%)	NM: 26 (37.1%) M: 25 (41%)	NM: 41 (58.6%) M: 30 (49.2%)	NM: - M: -
MD	11. Deal with misbehaviour	NM: - M: -	NM: 1 (1.4%) M: 1 (1.6%)	NM: 17 (24.3%) M: 10 (16.4%)	NM: 25 (35.7%) M: 27 (44.3%)	NM: 27 (38.6%) M: 20 (32.8%)	NM: - M: 3 (4.9%)
MD	12. Sticking with rules	NM: 1 (1.4%) M: 1 (1.6%)	NM: 5 (7.1%) M: 1 (1.6%)	NM: 15 (21.4%) M: 7 (11.5%)	NM: 25 (35.7%) M: 34 (55.7%)	NM: 24 (34.3%) M: 18 (29.5%)	NM: - M: -
MD	13. Threaten to discipline	NM: - M: 4 (6.6%)	NM: 4 (5.7%) M: 7 (11.5%)	NM: 19 (27.1%) M: 16 (26.2%)	NM: 27 (38.6%) M: 19 (31.1%)	NM: 20 (28.6%) M: 14 (23%)	NM: - M: 1 (1.6%)
MD	14. Time passes let it go (reversed-coded)	NM: 13 (18.6%) M: 17 (27.9%)	NM: 19 (27.1%) M: 13 (21.3%)	NM: 23 (32.9%) M: 11 (18%)	NM: 10 (14.3%) M: 14 (23%)	NM: 5 (7.1%) M: 6 (9.8%)	NM: - M: -

Note. HLE = Home Learning Environment; AUT = Autonomy support/expectations; MD = Management/discipline; NM = Non-migration background; M = Migration background.

A preliminary examination of the polychoric inter-item correlations with collapsed answer categories, calculated using the WLMSV estimator in Mplus, revealed similar numbers of correlations above .1 (or -.1 for negative correlations) in parents with and without a migration background (70 and 76 out of 91, respectively), for an overview see Table 7. In the group of parents without a migration background 22 correlations were of large effect size 23 were medium, and 25 were weak. In the group of parents with a migration background 20 were of large effect size 29 were medium, and 27 were weak. Items of the subscale Home Learning Environment (HLE) correlated strongly amongst each other in both groups of parents. Items of the subscale Autonomy Support (AUT) generally correlated strongly amongst each other in both groups of parents, as well. Correlations amongst the items of the Management/Discipline (MD) scale varied in both groups, see Table 7. We found weak to large correlations between items belonging to the subscale AUT with items belonging to the subscale MD and HLE and weak to medium correlations between items belonging to the subscales MD and HLE. Finally, Cronbach’s alphas for the three subscales were excellent for HLE and AUT (.83 and .86, respectively) and unsatisfactory for MD (.48). However, if item 14 was omitted from the MD subscale the Cronbach’s alpha was good (.75), see below.

Table 7. Inter-Item correlations Parenting Questionnaire of Parents with and without a Migration Background.

	2	3	4	5	6	7	8	9	10	11	12	13	14
1. Encourage to write	NM: .82 M: .76	NM: .66 M: .56	NM: .50 M: .65	NM: .34 M: .20	NM: .24 M: .38	NM: .16 M: .29	NM: .03 M: .32	NM: .26 M: .21	NM: .15 M: .36	NM: .05 M: .23	NM: .02 M: .08	NM: -.11 M: .15	NM: .04 M: .05
2. Encourage to do calculus	–	NM: .78 M: .57	NM: .68 M: .67	NM: .33 M: .16	NM: .38 M: .51	NM: .29 M: .46	NM: .19 M: .33	NM: .35 M: .30	NM: .18 M: .43	NM: −.10 M: .13	NM: .11 M: .23	NM: −.14 M: .16	NM: −.09 M: .00
3. Provide workbooks	–	–	NM: .50 M: .69	NM: .07 M: .03	NM: .19 M: .36	NM: −.02 M: .03	NM: −.19 M: .25	NM: .14 M: .18	NM: .01 M: .45	NM: −.01 M: −.03	NM: −.14 M: −.02	NM: −.09 M: .23	NM: −.06 M: −.21
4. Play number games	–	–	–	NM: .25 M: .29	NM: .46 M: .39	NM: .47 M: .39	NM: .34 M: .39	NM: .44 M: .31	NM: .24 M: .38	NM: .17 M: .24	NM: .34 M: .15	NM: .17 M: .09	NM: −.08 M: −.00
5. Respect child’s opinion	–	–	–	–	NM: .49 M: .54	NM: .61 M: .39	NM: .40 M: .55	NM: .54 M: .49	NM: .33 M: .48	NM: .07 M: .46	NM: .01 M: .14	NM: .14 M: .09	NM: −.15 M: .11
6. Encourage exploration	–	–	–	–	–	NM: .96 M: .63	NM: .80 M: .63	NM: .63 M: .58	NM: .66 M: .83	NM: .40 M: .40	NM: .30 M: .26	NM: .31 M: .36	NM: .01 M: .14
7. Encourage child to talk	–	–	–	–	–	–	NM: .92 M: .66	NM: .81 M: .71	NM: .81 M: .69	NM: .37 M: .49	NM: .37 M: .28	NM: .29 M: .21	NM: .05 M: –.06
8. Considerate of others	–	–	–	–	–	–	–	NM: .67 M: .88	NM: .79 M: .76	NM: .26 M: .33	NM: .37 M: .30	NM: .29 M: .19	NM: .05 M: –.01
9. Spend time with child	–	–	–	–	–	–	–	–	NM: .84 M: .69	NM: .46 M: .37	NM: .33 M: .30	NM: .38 M: .13	NM: −.12 M: .12
10. Child to be responsible	–	–	–	–	–	–	–	–	–	NM: .53 M: .34	NM: .34 M: .29	NM: .31 M: .40	NM: .03 M: .07
11. Deal with misbehaviour	–	–	–	–	–	–	–	–	–	–	NM: .66 M: .40	NM: .74 M: .45	NM: −.07 M: −.08
12. Sticking with rules	–	–	–	–	–	–	–	–	–	–	–	NM: .72 M: .56	NM: −.02 M: .03
13. Threaten to discipline	–	–	–	–	–	–	–	–	–	–	–	–	NM: .03 M: .30
14. Time passes let it go (reversed-coded)	–	–	–	–	–	–	–	–	–	–	–	–	–

Note. NM = Non-migration background; M = Migration background.

Testing the factor structure of the parenting questionnaire

To check whether the original factor structure of the Parenting Questionnaire held in our sample we fitted the three-factor model to the total sample prior to investigating MI. In this model, we assumed the 14 items formed three original subscales, with each subscale representing one dimension of home-based parental involvement style. The resulting model fitted the data well (χ²=88.19, df = 74, p = .12; RMSEA = .04; CFI = .99; TLI = .99). The correlation between HLE with AUT was .38 (p < .001); the correlation between HLE and MD was .13 (p = .22); and the correlation between AUT and MD was .49 (p < .001). Further, all factor loadings were significant (p < .001) except for the factor loading of item 14 from the MD subscale (‘When a lot of time passes after my child misbehaves, I just let it go’, est(SE)= −0.05 (0.11), p = .64). This corresponded with participants’ experiences that they did not understand the item. Therefore, item 14 was removed from further analyses.

Next, we tested whether the three-factor structure holds similarly in the two subgroups of parents with and without a migration background by applying the four steps of MI testing. The three-factor model, with different parameter estimates allowed in the two groups, initially did not converge. When inspecting the correlation structure and potential overlap of the content of the items, it became clear that item 2 ‘encourage to do calculus’ did not add unique information to the HLE construct, as item 1 also stresses ‘encouraging the child’ and item 3 also concerns calculus ‘providing calculus workbooks’. Therefore, we decided to drop item 2 from further analyses. Further, item 7 ‘encourage to talk’ showed high correlations with items 6 ‘encourage exploration’ and 8 ‘considerate of other’ in both groups, particularly in the non-migration background group. However, comparing the content of the items, we decided that item 7 may contribute new information, as none of the other items concern the child talking about his/her feelings. We, therefore, chose to constrain the factor loadings of items 6, 7, and 8 to each other in the first step of the measurement invariance testing (the configural invariance model). After these changes, the model converged well. Results from fitting the three-factor model to the data, including the subsequent different stages of MI tested across the two subgroups, are given in Table 8. Estimates of the unconstrained thresholds, factor loadings and residual variances from the configural invariance model are given in Table 9. The fit of this model was mediocre to good (χ² = 145.69, df = 104, p = .004; RMSEA = .08; CFI = .98; TLI = .97). We, therefore, accepted the configural invariance model and concluded that the three-factor structure holds across parents with and without a migration background. Parameter estimates in this model were generally similar in both groups, but with some differences. For the HLE factor, item 4 ‘play number games’ appeared a stronger indicator of HLE in the migration background group than in the non-migration background group of parents. Somewhat larger differences in factor loadings and residual variances between groups occurred for items 6, 7, and 8, belonging to the AUT factor, appearing to be stronger indicators with less residual variance in the non-migration background group than in the migration group. With regard to items from the MD factor, factor loadings also were somewhat higher for the non-migration background group, and residual variances somewhat lower.

Table 8. Measurement Invariance Results for the Parenting Questionnaire in Parents with and without a Migration Background.

	χ²	df	p	RMSEA	CFI	TLI	Δχ²	Δdf	ΔRMSEA	ΔCFI
Configural invariance	145.69	104	.004	.078	.98	.97
Metric invariance	158.23	113	.003	.078	.98	.97	15.12	9	0	.001
Scalar invariance	196.86	140	.001	.079	.97	.97	46.98	27	.001	.006
Strict invariance	177.23	128	.003	.077	.98	.97	22.89	12	.002	.004

Note. χ² = adjusted chi-square test statistic; df = adjusted degrees of freedom; p = p-value; RMSEA = root mean square error of approximation; CFI = Comparative Fit Index; TLI = Tucker-Lewis Index; Δχ² = Adjusted chi-square difference between the fitted model and the comparison model (configural invariance model); Δdf = Adjusted difference in degrees of freedom between fitted and comparison models; ΔRMSEA = Difference in root mean square error of approximation; ΔCFI = Difference in Comparative Fit Index. RMSEA value smaller than 0.05 good fit, between 0.05 and 0.08 adequate fit, and between 0.08 and 0.10 mediocre fit. Values larger than 0.10 are not acceptable (Van de Schoot, Lugtig, and Hox 2012.; Yu 2002). For CFI and TLI, values larger than 0.95 indicate good fit, values between 0.95 and 0.90 mediocre fit. Values smaller than .90 are not acceptable (Van de Schoot, Lugtig, and Hox 2012.). Changes in RMSEA of .015 and in CFI of -.01 are acceptable (Chen 2007).

Table 9. Parameter estimates From the Two-Group Confirmatory Three-Factor Model fitted to data on the Parenting Questionnaire in Parents with and without a Migration Background.

		Unstandardized factor loadings		Residual variances
Factor	Item description	Non-migration background	Migration background	Non-migration background	Migration background
HLE	1. Encourage to write	1.10	1.10	0.45	0.48
HLE	3. Provide workbooks	0.88	1.07	0.52	0.45
HLE	4. Play number games	1.40	2.27	0.38	0.16
AUT	5. Respect child’ s opinion	0.61	0.74	0.71	0.67
AUT	6. Encourage exploration	3.26	1.62	0.09	0.26
AUT	7. Encourage child to talk	3.26	1.21	0.09	0.40
AUT	8. Considerate of others	3.26	1.91	0.09	0.19
AUT	9. Spend time with child	1.61	1.67	0.26	0.28
AUT	10. Child to be responsible	1.55	2.05	0.28	0.21
MD	11. Deal with misbehaviour	1.71	1.36	0.24	0.39
MD	12. Sticking with rules	1.32	0.75	0.44	0.55
MD	13. Threaten to discipline	1.70	0.85	0.19	0.66

The next step showed that the fit of the metric invariance model was not worse when factor loadings were constrained (Δχ² = 15.12, Δdf = 9, p = .09; ΔRMSEA = 0 and ΔCFI = .001). Metric invariance is held across parents with a migration background and parents without a migration background. To test for scalar invariance, the thresholds were constrained. In this step, the fit did worsen significantly (Δχ² = 46.98, Δdf = 27, p = .01; ΔRMSEA = .001 and ΔCFI = .006). The Parenting Questionnaire did not reach scalar invariance with respect to parents with a migration background and parents without a migration background. However, when the thresholds of item 13 ‘threaten to discipline’ were not held equal across groups, the scalar factorial invariance model described the data reasonably well (χ² = 185.602, df = 137, p = .003; RMSEA = .074; CFI = .98; TLI = .98). Additionally, the fit was not significantly worse than the metric invariance model (Δχ² = 31.25, Δdf = 24 p = .15; ΔRMSEA = .004; ΔCFI = .002). On a scalar invariance level, the thresholds can be considered equal across these two subgroups, except for item 13 ‘threaten to discipline’. This means a higher score on an item is due to a higher score on the latent construct in both groups, and not due to any measurement differences between the two groups. This allows for the careful comparison of differences in mean factor scores between the two groups. With the release of the thresholds of item 13 strict invariance was also reached, meaning differences in residual variances in the two subgroups were not insuperable, see Table 10.

Table 10. Model Fit for All Levels of Measurement Invariance Tested Across Migration Background the thresholds of item 13 not held equal across groups.

	χ²	df	p	RMSEA	CFI	TLI	Δχ²	Δdf	ΔRMSEA	ΔCFI
Configural invariance	145.69	104	.004	.078	.98	.97
Metric invariance	158.23	113	.003	.078	.98	.97	15.12	9	0	.001
Scalar invariance	185.60	137	.003	.074	.98	.98	31.25	24	.004	.002
Strict invariance	171.14	125	.004	.075	.98	.98	171.14	12	0	.001

Note. χ² = adjusted chi-square test statistic; df = adjusted degrees of freedom; p = p-value; RMSEA = root mean square error of approximation; CFI = Comparative Fit Index; TLI = Tucker-Lewis Index; Δχ² = Adjusted chi-square difference between the fitted model and the comparison model (configural invariance model); Δdf = Adjusted difference in degrees of freedom between fitted and comparison models; ΔRMSEA = Difference in root mean square error of approximation; ΔCFI = Difference in Comparative Fit Index.

Discussion

Home-based parental involvement may help to close the achievement gap between children with and without a migration background (Bakker et al. 2013; de Winter-Koçak and Badou 2020; Zumbuehl and Dillingh 2020). Current findings contribute to articulating and operationalizing both home-based parental involvement activities and home-based parental involvement style for parents with and without a migration background in the Dutch kindergarten context enabling comparative studies. First, home-based parental involvement activities vary and should be described along at least two distinct dimensions. Our first dimension ‘Learning through play’ reflects an informal type of involvement, including ‘Playing with the child’, ‘Reading to the child’, and ‘Telling stories to the child’. Our second dimension ‘Support of learning’ reflects a formal type of involvement, including ‘Supervising the child’s work for school’ and ‘Practicing words, number, or concepts with the child’. Because parents with a migration background might rely more on informal activities in supporting their child’s learning, adding an ‘Informal subscale’ to the Quantitative Home-based Involvement Questionnaire can help to make involvement practices and cultural capital provided by parents with a migration background visible which would otherwise have remained hidden (McWayne 2015; McWayne, Foster, and Melzi 2018; Pels and De Haan 2007). The subscale ‘support of learning’, which showed unsatisfactory reliability, might benefit from further modification, followed by re-exploration of the overall factor structure (Ponterotto and Ruckdeschel 2007). Subsequently, the proposed factor structure and investigation of measurement invariance across parents with and without migration background and SES levels for this questionnaire should be conducted in an independent sample drawn from the same population of Dutch parents (Fokkema and Greiff 2017).

The second main finding is that the Parenting Questionnaire replicates the three-factor structure identified by Hindman and Morrison (2012). The Parenting Questionnaire assesses home-based parental involvement style by differentiating three facets of parenting that can contribute to child development: home learning environment, support for autonomy and expectations for appropriate behaviours, and management and discipline. Furthermore, results indicate this questionnaire to be largely measurement invariant across parents with and without a migration background, except for one item of the scale. This implies that scores obtained with this questionnaire can be confidently used to compare these two groups, as any group differences in scores can be taken to reflect true differences in parents’ home-based involvement styles, rather than differences in measurement across groups caused by cultural conventions, differential social desirability across groups, or a lower language ability (Putnick and Bornstein 2016; Van de Vijver 2015).

However, it should be noted that only when adjustments were made to the questionnaire (such as omitting two items and releasing the thresholds of item 13 ‘threaten to discipline’) we were able to reach sufficient levels of MI to compare groups. This calls for more research on MI of this instrument, preferably in larger samples that enable further distinction according to ethnic background and immigration history.

Limitations and considerations for future research

Limitations of this research should also be noted. First, our sample was very diverse, but not sufficiently large to further explore or test the factor structure of the two home-based parental involvement questionnaires in more than two subgroups based on the migration background of the parents. Compared to the native Dutch group, relatively larger within-group differences might exist in the group of parents with a migration background as it consists of different origin groups. Earlier studies found group differences in home-based parental involvement activities shown between immigrants from different subgroups (Kim et al. 2018). Garcia Coll and colleagues (2002), for example, described differences in parental involvement of parents from three migrant groups in the US (Portuguese, Dominican, and Cambodian) and suggested these might be explained by differing forms of group migration (voluntary labour migrants or refugees), the educational system’s differential responses to the groups, and group differences in cultural values.

A related limitation is that we were unable to additionally test for MI across SES. Our migration and non-migration background subsamples differed significantly on SES. This means that the instrument can be used in samples with diverse migration backgrounds, as SES is known to correlate with migration background and can thus be a population characteristic. Measurement invariance across SES groups awaits further research, however. Differential effects of SES on academic outcomes have been reported for parents with and without a migration background. Loboda, Vogelbacher, and Gawlitzek (2017) found for example, that in German parents without a migration background, SES has a stronger association with language proficiency than parenting style. Among parents with a migration background, SES showed no direct association with language proficiency while parenting style did show a direct association. As such, future studies are needed to test the instrument for MI across SES. If no measurement invariance is found across SES, an imbalance in SES across migration background and non-migration background subsamples might conflate or distort potential differences in home-based parental involvement.

With regard to the PCA of the Quantitative Home-Based Involvement Questionnaire, the Cronbach’s alpha of the ‘Support of learning’-subscale was unsatisfactory. This is reflected in the inter-item correlations as well, which suggest that if parents reported doing certain activities with a high frequency, other activities in the same scale were not reported as high frequent. Items in the ‘Support of learning’-subscale represent a wide variety of activities; from supervising school work to going to the library. To increase the reliability estimate it might be useful for future studies to add items and re-explore the instrument’s factor structure (Ponterotto and Ruckdeschel 2007). Additionally, the PCA initially suggested a four-factor solution. One of the four components consisted of language/literacy items. Although cross-loadings were found as well, this may indicate that these particular items form the basis of a separate scale focusing on language and literacy. As such, increasing the number of items might allow for different dimensions of home-based parental involvement to be detected. These clusters may differ across age groups as well. For example, reading acquisition becomes less important as children get older, whereas for older children, help with school-/homework might grow in importance. Future studies could, therefore, explore the factor structure across age groups.

Concerning the Parenting Questionnaire, we were able to reach sufficient levels of measurement invariance to compare groups, however not without making small adjustments. The nature of home-based parental involvement changes with children’s age (Bakker et al. 2013). As the current study focused on support of learning in children of kindergarten age (4–5 years-old), differences between the specific behaviours represented by the items 1–3 might not be meaningful at this age. A comparable age group was used for the development of this version of the questionnaire by Hindman and Morrison (2012). However, as no inter-item correlations are given in their report it is unknown whether similar problems occurred in their study. Future research could include a sample more diverse in age to investigate whether differences between the specific behaviours represented by the items then increase, hence decreasing inter-item correlations. Another possibility would be to investigate whether item 2 can be combined with item 1 to form the item ‘I encourage my child to learn/study’.

Additionally, we needed to collapse response categories to perform the MI analyses as too many empty cells or cells with fewer than five observations occurred in the crosstabs when we divided the sample over two groups. We collapsed as few categories as possible to maximize information on the variation in item scores. Low variance in the item scores may indicate that the number of answer categories should be increased. Further research in a larger and more heterogeneous sample may help to increase variation in item scores and allow for better judgement of the suitability of the answer categories.

Implications for educational practice

Findings support the idea that home-based parental involvement activities may be assessed in a more inclusive way across different origin groups than has been done in studies to date. Furthermore, our study provides researchers with an instrument to measure home-based parental involvement style equivalently across parent populations with and without a migration background. Even though the instruments described in this study can benefit the assessment of home-based parental involvement, researchers and educational practitioners should be aware that the instruments operationalize a limited set of home-based parental involvement activities. Additionally, self-report instruments only present the parent’s perspective. Self-reported involvement, for example, may or may not be contingent to the child’s cues and emotional and instructional needs (Pino-Pasternak and Whitebread 2010). We, therefore, encourage teachers and other practitioners in the field of early education to enter into a reflective dialogue with parents that have dissimilar backgrounds to mutually explore their home-based involvement and the dominant and non-dominant cultural capital these parents can transmit to their children in the family context to support children’s development. This may allow teachers to strengthen parents’ home-based involvement as well as provide teachers with insights into cultural variations in involvement practices and their potential (Iliás et al. 2016; Kristen et al. 2011). This is especially important when children have their first real encounter with the host nation’s culture upon entering kindergarten. Such interactions may allow teachers and parents to connect these children’s school and family worlds whilst employing available funds of knowledge, sensitive to the cultural capital of parents with different backgrounds, and acknowledging the value of different parental involvement practices (Leopold and Shavit 2013; McWayne 2015; Pak and Vandekerckhove 2016).

Data availability

The data that support the findings of this study are available from the author, A.M. Willemen, upon reasonable request.

Disclosure statement

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

Additional information

Funding

This work was supported by The Netherlands Initiative for Educational Research [grant number: 405-14-572] and the Amsterdam municipality [grant number: 10000780]. The sponsors had no role in the study design; in the collection, analysis and interpretation of data, in the writing of the report, and in the decision to submit the article for publication.