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The multidimensional model of Maori identity and cultural engagement: measurement equivalence across diverse Maori groups.

The field of quantitative identity research has undergone somewhat of an emic (by the people of the culture, for the people; Berry, 1989) revolution in recent years. The addition of the Pacific Identity and Wellbeing Scale (the PIWBS; Manuela & Sibley, 2013; 2015a), and the Multidimensional Model of Maori Identity and Cultural Engagement--Revised (the MMM-ICE2; Houkamau & Sibley, 2010, 2015a), have allowed researchers to assess identity in a culturally-specific and nuanced way. The MMM-ICE2 is a seven dimension, public domain, quantitative, Likert-style, self-report measure created for Maori by Maori (Houkamau & Sibley, 2010, 2015a). The purpose of the scale is to measure one's subjective identification as Maori (Houkamau & Sibley, 2010, 2015a). The MMM-ICE2 has shown utility in predicting a wide range of outcomes including: home-ownership (Houkamau & Sibley, 2015b), Marae visits and fluency in Te Reo Maori (Houkamau & Sibley, 2010), perceptions of National and Personal well-being (Houkamau & Sibley, 2011), self-esteem (Matika, Manuela, Muriwai, Houkamau, & Sibley, 2017), environmental attitudes and values (Cowie, Greaves, Milfont, Houkamau, & Sibley, 2016), and mental health (Muriwai, Houkamau & Sibley, 2015). Here, we aim to test the measurement equivalence of the MMM-ICE2 across urban/rural Maori, gender, "age and" sole-identified versus mixed Maori, to provide evidence that the scale is measuring subjective identification equally across groups.

Development of the MMM-ICE

Initially, Houkamau and Sibley (2010) aimed to create a scale of Maori identity, where identity is defined as: "constituting those aspects of the self-concept (including beliefs/values/ attitudes) that pertain to 'who' a person is as Maori, how they 'fit in' with others in the social world and what that means in terms of behaviour" (Houkamau & Sibley, 2010, p. 12). The original items were from a broad and detailed review of the literature on Maori identity and the international literature on ethnic identity. The initial item pool included items based on: identity centrality (Sellers, Smith, Shelton, Rowley, & Chavous, 1998; Luhtanen & Crocker, 1992), collective self-esteem (Luhtanen & Crocker, 1992), cultural efficacy (see Durie, 1995), active identity engagement (based on qualitative research by Houkamau, 2006), spirituality (i.e., Durie, 1994), interdependency/collectivism (Kashima & Hardie, 2000), and essentialist/ authenticity based beliefs (based on discussions on the legitimising myth of real "Maoriness" by Borrell, 2005; Chadwick, 1998).

Houkamau and Sibley (2010) then used Exploratory Factor Analysis (EFA) on responses to a pool of 92 items by 270 participants recruited on the internet. EFA is a method used to explore how items cluster together to form a number of latent dimensions. A six-factor solution emerged from the analysis, meaning there were six reliable dimensions which underlie Maori identity over 47 items drawn from the data. Descriptions of the different dimensions can be found in Table 1. The first dimension was called Group Membership Evaluation (GME), which relates to having positive feelings about one's membership in the group 'Maori'. A second aspect of this dimension is how central and important to the self one's identity as a 'Maori' is. Another dimension was named Socio-Political Consciousness (SPC). This dimensions indexes beliefs in the continued importance of colonial history and the injustices experienced by Maori. This dimension also assess the degree to which the participant feels they actively engage in the political process and 'stand up' for Maori political rights. The dimension of Cultural Efficacy and Active Identity Engagement (CEAIE) measures the extent to which one believes they have the personal resources to engage with other Maori in traditional cultural contexts.

The fourth dimension of the scale was named Spirituality, which measures engagement with traditional Maori concepts of spirituality like recognising tipuna (ancestors) and that which is tapu (sacred). The fifth dimension was called Interdependent Self-Concept; this assesses the degree to which the participant believes that being Maori is interdependent or independent from their relationships with other Maori. Put more simply, it assesses whether one feels they need to actively engage with other Maori in order to truly be Maori. The final dimension was named Authenticity Beliefs. This dimension assess the degree to which someone believes that Maori have to do certain cultural things or look/ act certain ways to be an authentic Maori.

In a later paper, Sibley and Houkamau (2013) examined the scale properties of the MMM-ICE, and assessed the stability of the scale across genders, and across the lifespan. They extended the initial analyses by using item response theory to look at the scale's internal reliability. That is, to check if there were scale reliability differences between people and at different levels of the dimensions. The MMM-ICE tended to be most precise at the mean level range of each dimension, but each dimension showed an acceptable level of reliability across the scale. Examining the dimensions across age cohorts and genders provided interesting comparisons and insights into how identity may change with age (although longitudinal research is needed). Older people tended to have a higher level of identification with the MMM-ICE dimensions and across genders the results were reasonably similar.

Finally, due to feedback from the community and further examination of the literature, Houkamau and Sibley (2015a) updated the original MMM-ICE by adding a seventh factor, Perceived Appearance. Perceived Appearance assesses the extent to which someone believes that they looking prototypically Maori to others. Houkamau and Sibley (2015a) also showed that this new factor, when controlling for the other six dimensions of the MMM-ICE2, predicted unique variation in reported perceived discrimination and that people lower in this dimension were more likely to be of mixed Maori-Pakeha (New Zealand European) descent. However, despite the growing body of research developing the scale, some important questions remain: for example, does the MMM-ICE2 measure identity as 'well for urban Maori as it does for rural Maori? What about for men versus women? Or across age groups? And, finally, for those who solely identify as Maori versus those who also identify with other ethnicities?

The aim of this paper is to test the measurement equivalence of the MMM-ICE2 across all of these groups using Multigroup Confirmatory Factor Analysis (MCFA).

Maori Identity: Key Influential Variables

MCFA is a tool that allows us to test the factorial equivalence of the MMM-ICE2 subscales across groups. However, the researchers must still choose suitable groups for comparison. For example, Manuela and Sibley (2015b) chose to compare the Pacific Identity and Wellbeing Scale across the major Pacific Island groups (Samoan, Cook Island, Tongan, and Nuiean). For the study of Maori identity this decision is less clear cut (especially since there are numerous iwi). However, several key variables have been identified in past literature as having a role in shaping one's identity as Maori.

Urban and Rural Maori

The distinction between urban and rural Maori has been influential in past research on identity. This distinction has been largely shaped by historical forces (Durie, 1994, Houkamau, 2006, 2010). A key time period in the shaping of modem Maori identity is said to have occurred in the middle of the 20th century, where there was a mass migration away from (rural) ancestral lands to urban areas for economic opportunities (Taonui, 2012). This transition meant that assimilation of Maori into Pakeha culture became a reality of Maori life for some. For example, it was official policy to 'pepper pot' state housing (meaning dispersing Maori families throughout Pakeha ones). Additionally, speaking te reo Maori in schools became a punishable offense and the amount of land owned by Maori shrunk to the point that the remaining Maori-owned lands could only support one quarter of the Maori population (Belgrave, 2005; Walker, 1990). The distinction between rural and urban Maori was pronounced through this time in history as many who resided in urban areas adapted to Pakeha culture as they had reduced access to Maori cultural resources. Whereas rural Maori were said to still be engaged in Te Ao Maori, or the traditional Maori world/way of life (Houkamau, 2006, 2010).

However, these events led to 'the Maori Renaissance', a phrase used to refer to a period in New Zealand history from approximately the late 1960s through until the 1990s where Maori fought back against the forces of assimilation (Derby, 2014; Taonui, 2012). As a consequence, the Government responded with policies promoting Maori culture and biculturalism, and established the Waitangi Tribunal to address Treaty violations (Belgrave, 2005; Derby, 2014). The urbanization that contributed to a weakening of traditional Maori identity (Durie, 1994; Houkamau, 2006, 2010) also aided in the creation of this movement, as over the years, Maori became more concentrated in urban centers (Taonui, 2012).

Although, through this period Maori culture became more easily accessible to urban Maori than it had in the past, there still remains the possibility that Maori from rural areas have different conceptualizations of Maori identity than urban Maori. That being said, recent research with the MMM-ICE2 has found no differences between the urban/rural divide across common patterns of Maori identity (Greaves, Houkamau, & Sibley, 2015). In contrast, Chapple (2000) argues that the urban/rural divide exists and now may be more of a class distinction comprising an urban, educated, working class of Maori, versus rural Maori that have few employment prospects. Other research has found that there are differences in health risk factors across rural and urban Maori (Hodgkin, Hamlin, Ross, & Peters, 2010; Robson, Cormack, & Purdie, 2010), including that urban Maori youth are at a higher risk of developing depression (Clarke, & Jensen, 1997). Therefore, due to the possible different experiences that rural and urban Maori may have, it is beneficial to test the measurement equivalence of the MMM-ICE2 over this divide.


Life experiences and how people perceive one another typically differ depending on one's gender; of course this is no different for the experiences of Maori. Although, research using the MMM-ICE2 rarely finds gender differences across the scale. The most thorough investigation of gender differences being Sibley and Houkamau's (2013) examination of the stability of the scale across the lifespan by gender. They used item response theory to check if there were scale reliability differences between people, and at different levels of the dimensions. The MMM-ICE2 tended to be most precise at the mean level range of each dimension, but each dimension showed an acceptable level of reliability across the scale. Importantly, across genders the results were reasonably similar.

While there is little quantitative work focusing on Maori women's identity, a body of qualitative work recognises that Maori women's experience and identity have been greatly shaped by their gender. Work completed under the mana wahine framework of kaupapa Maori research challenges the idea that women have held, or hold, a lower status position in Maori society (Pihama, 2001). Mana wahine provides a framework for research that acknowledges issues that impact specifically on Maori women and girls (Pihama, 2001; Simmonds, 2011). For example, experiences of reproduction alone are inherently life-and identity- shaping for Maori women (Le Grice, 2014). Thus, although there is little quantitative research on Maori identity and gender, extant research, combined with the qualitative and theoretical literature suggest that gender is an important category to assess the MMM-ICE2 across.


Historical events have been found to be very influential in shaping Maori identity. Houkamau (2006, 2010) showed that identity is linked to socio-historical contexts in that cultural, social, political and historical processes shape identity over time and across generations. As such, age cohort groups may have had very different experiences relating to their identities. Houkamau (2006, 2010) interviewed 35 Maori women, and found that three key periods of events in New Zealand history were salient in their descriptions of identity. These three key periods of events influenced the identity development for these three distinct age cohort groups. Firstly, there was an older group who felt positive about their Maori Identity and engaged in the traditional Maori world. Secondly, there was a middle-aged group who grew up in a time when Maori Identity was devalued, who struggled to form a sense of identity, and felt removed from their culture. This group were the least likely to feel that they could confidently rebut racism and negative views of Maori. Thirdly, there was a younger group who grew up during the Maori Renaissance, and so were able to learn how to act competently as Maori and were also able to navigate a colonised or 'Pakeha' world.

Quantitative research has also shown age differences in Maori identity, although it is as yet unclear whether these were cohort effects or if identity changes as one ages. Sibley and Houkamau (2013) investigated the stability of the MMM-ICE2 across the lifespan and found that older people tended to have higher scores across MMM-ICE2 dimensions. Greaves and colleagues (2015) also found that those with an enculturated (higher scoring) identity profile tended to be older. Thus, keeping in mind the historical influences on identity and the higher level of identification that past research has found with older people, age may have an influence on MMM-ICE2 scale scores. Therefore, we aim to test the measurement equivalence of the MMM-ICE2 across three age cohorts based on Houkamau (2006, 2010): those aged under 40 (post-Maori Renaissance and may have benefitted from policies for increased biculturalism), 41-54 (formative years during the Maori Renaissance) and over 55 (pre-Maori Renaissance).

Sole and Mixed Maori

Another key variable that influences ethnic identity is whether one identifies solely as Maori or also identifies with another ethnicity (typically Pakeha). In 1974, being officially 'Maori' first legally moved beyond a Western blood-quantum based framework, which assumes that Maori identity and culture have a strict biological basis, to one of identification and affiliation (Cormack & Robson, 2010; Durie, 1994; Kukutai, 2004). A blood-quantum based system meant that one had to have a minimum level of Maori ancestry to identify as Maori. For example, one had to be at least half Maori (i.e. have one Maori parent) to identify their ethnicity as Maori. However, post-1974 anyone with whakapapa (with a Maori ancestor) could be counted officially as Maori on birth certificates and documentation, on the electoral roll (from 1975), and on the census if they wished (from 1986). Even though, in reality, Maori had been doing this for years (Durie, 1994). The 1991 national census even allowed people to identify with their iwi and distinguished between a) having a Maori ancestor and b) choosing to identify as Maori under ethnicity (including mixed- and sole-Maori). These changes to the official conception of ethnicity in New Zealand meant that being Maori moved from being about the Western and outdated concept of 'race' and toward ethnic identity or affiliation.

In the present day one in seven New Zealanders (14.9%) identify as Maori (although a further 100,000 New Zealanders report Maori ancestry but do not identify as Maori), with almost half (46.5%) of these individuals identifying solely as Maori (Statistics New Zealand, 2013). The experiences of mixed and sole identified Maori may differ as those who identify with another ethnicity may be able to draw upon the 'cultural resources' of the other ethnicity (Houkamau & Sibley, 2014). This effect is particularly pronounced for those who also identify as Pakeha, who are the majority of the population in New Zealand. These individuals may have a broader repertoire of psychosocial resources that can help them interact effectively with Pakeha and Maori (Houkamau & Sibley, 2014; Kukutai, 2007, 2013; Kukutai & Callister, 2009; Kukutai & Zealand, 2008; Muriwai et al., 2015).

As a result, research has found differences between sole-identifying and mixed- identifying Maori. It may be due to higher levels of racism that sole-identified Maori are more likely to experience exclusion (Houkamau & Sibley, 2015a; Nairn & McCreanor, 1991; Pihama, 2001; Thomas & Nikora, 1996) which can lead to a range of negative psychological outcomes (Houkamau & Sibley, 2014; Muriwai et al., 2015). Houkamau and Sibley (2014) have also shown that mixed and sole identifying Maori differ in some political attitudes: sole identifying Maori showed higher support for the Maori party, more warmth towards Maori and more support for policies benefitting Maori (Houkamau & Sibley, 2014). Due to these consistent findings of differences between sole-and mixed-identifying Maori over a range of outcomes, it is important to test the measurement equivalence of the MMM-ICE2 across these groups.

Testing Measurement Equivalence

A key goal in the development of the MMM-ICE was to create a scale to assess one's subjective Maori identity. Maori, however, are a diverse and changing group. In earlier Maori identity research, Durie (1995) recognized this as a key assumption when creating a Maori identity scale for the Te Hoe Nuku Roa study of Maori households. Furthermore, research with the MMM-ICE2 has also shown that Maori identity can be expressed in a number of diverse patterns (Greaves et al., 2015). This previous research highlights the need to test the factor equivalence of the MMM-ICE2 over a diverse number of groups within Maoridom to ensure that the scale can serve each sector of the Maori community equally. For example, if Maori residing in rural areas interpret items from the MMM-ICE2 differently to those who reside in cities/urban areas then the sub-scales are referring to different concepts. Meaning, that the whole point of the scale--to measure certain factors within, and specific to, Maori ethnic identity--is compromised. Manuela and Sibley (2015b) liken this to the problems researchers have using Western scales, like self-esteem, across different cultural contexts and languages. That is, the scale could potentially lose its meaning when items do not 'translate' across contexts and therefore the scale may not actually measure the construct that researchers had intended to measure.

A Multigroup Confirmatory Factor Analysis (MCFA) extends typical Confirmatory Factor Analysis (CFA) and tests factorial equivalence by estimating a CFA model for separate groups at the same time. This allows the researcher to test measurement equivalence (sometimes called measurement invariance) or whether the scale assesses the same constructs across the different groups (for more on MCFA see Cheung & Rensvold, 2002; Steenkamp & Baumgartner, 1998; for a review of measurement invariance see Vandenberg & Lance, 2000). In our case, one model we aim to test is the MMM-ICE2 across age cohort groups. Thus, we would estimate fit across the three theoretically different a priori specified age categories (40 and under, 41-54, and 55 plus), the goal being that the model fits equally well across groups. There are three levels at which this can be assessed: configural, metric, and scalar equivalence (see Milfont & Fischer, 2015).

Configural equivalence is the least conservative measure of factor equivalence. A key purpose of configural equivalence is to establish a baseline model for more stringent tests of measurement equivalence (Vandenberg & Lance, 2000). Good configural equivalence would indicate that different groups are interpreting the construct the researcher is testing for in the same way, or that the items are measuring the same underlying concepts across groups. If researchers do not find configural equivalence, then the measure represents different constructs in different groups, and so it becomes pointless to assess metric or scalar equivalence (Vandenberg & Lance, 2000). In MCFA, the test of metric equivalence examines the extent to which the factor loadings are the same across the groups. Metric equivalence assesses whether the strength of the relationship between the indicators (Likert items, in our case) and the underlying latent construct are the same across different groups. If the tests of metric equivalence are satisfied then the groups can be compared with the confidence that the measurement units (in our case, the intervals of the Likert scale) are comparable across groups.

The third and most demanding test of factorial equivalence is that of scalar equivalence. Scalar equivalence extends the other model by estimating the extent to which the intercepts for the indicators are similar across groups. To return to our example of testing the scale across age cohorts, scalar equivalence would tell us if the mean scores (intercepts) of the different survey items are comparable across everyone regardless of age. For example, two people from different age groups (e.g., one under 40 and one aged 55 plus) have conceptually the same level of belief in the continued importance of the Treaty of Waitangi and both actively stand up for Maori political rights (indexed as part of the MMM-ICE2 by the subscale/construct of Socio-Political Consciousness). These two individuals should have a similar mean score on any given question in the Socio-Political Consciousness subscale. In other words, we would hope that the average construction of Maori identity for one group is not dramatically different from another when using the MMM-ICE2 scale, except when there are real mean differences between groups.


In this paper we aim to test the measurement equivalence of the MMMICE2 with four Multigroup Confirmatory Factor Analyses looking across the urban/ rural divide, gender (male or female), three age cohort groups (under 40, 41-54, and 55+) based largely on work by Houkamau (2006, 2010), and sole-Maori or mixed-Maori ethnic identification. Additionally, this paper presents the first Confirmatory Factor Analysis of the MMM-ICE2 (revised) scale. The MMM-ICE2 is a scale of Maori identity that was created based on the recognition that Maori are a broad and diverse group (Houkamau & Sibley, 2010). As such, we hypothesise that the MMM-ICE2 will display fairly good measurement equivalence across all groups.


Participant Details

Participants were 436 women, 260 men with a mean age of 44.01 (SD=13.03; note that sample sizes varied across analyses due to missing data). We sampled participants that identified as Maori, however, 55% also identified as Pakeha (NZ European; n=383), 5.6% as Pasifika (n=39), 1.3% as Asian (n=9), and 1.4% as another ethnicity (n=10). Participants were asked if they identified with a religion or spiritual group, 44.4% of the sample identified as religious (n=309). In regards to education, 25.1% did not report their highest level of education or reported no education (n=175), 33.3 % reported at least some high school (n=232), 18.0% reported having studied towards a diploma or certificate (n=125), 17.1% reported having studied at the undergraduate level (n=119), and 6.5% reported having pursued post-graduate study (n=45).

Participants' postal addresses were used to identify the levels of material deprivation for each participant's immediate neighbourhood area based on census data (Atkinson, Salmond, & Crampton, 2014). The sample had a mean NZ Deprivation 2013 score of 6.77 (SD=2.78). The index is decile ranked (each unit represents 10% of the population) from 1 to 10 (low-high), therefore a mean score of 6.77 indicates a moderate level of deprivation relative to others in New Zealand. We also used participant addresses to determine whether each participant lived in either a rural or urban unit as defined by the Local Government Act 2002 (Statistics New Zealand, 2014). People living in urban areas constituted 52.8% of the sample (n=366), and those in rural areas were 47.2% of the sample (n=327).

Sampling Procedure

As part of the Time 4 New Zealand Attitudes and Values Study (NZAVS) sampling design, we included a booster sample aimed specifically at recruiting Maori participants (Frame 5 of the Time 4 NZAVS). This sample frame consisted of 9,000 people randomly selected from those who indicated on the 2012 Electoral Roll that they were of Maori descent. A total of 690 participants responded to this booster sample.

Adjusting for the overall address accuracy of the electoral roll as a whole, this represents a response rate of 7.78%. It should be noted that this response rate is lower than that observed for the main (full random probability) sample frames used in the NZAVS, which give responses rates of up to approximately 16%. The low response rate for this sample likely indicates many factors, among the most influential being the overall reduced likelihood of Maori participants to respond to postal surveys in general, combined with the possibility that contact details for Maori in the electoral roll may, on average, have a lower level of accuracy. It is likely that this relatively low response rate was also partially affected by the fact that people were opting into a 15-year longitudinal study. Thus, providing their contact details indicated that they were willing to be contacted by us to complete similar questionnaires for the next 15 years.

The questionnaire administered to the NZAVS Maori booster sample was similar in format and content to the standard NZAVS questionnaire, except it included questions specifically designed for Maori, and the cover letter introduced the survey as a "The NZAVS--Maori Identity Focus Questionnaire." The lead researcher and point of contact for this sample frame was of Maori descent, and was introduced to participants in the cover letter by listing iwi affiliations. Participants were informed that they had been randomly sampled for this study from among those who indicated that they were of Maori descent on the electoral roll.

Questionnaire Measures

Participants completed the full 54 item MMM-ICE-Revised including reverse-scored items and subscales for all seven subscales (Houkamau & Sibley, 2015a). A full copy of the scale is presented in the Appendix. Group Membership Evaluation (GME) was assessed by eight items ([alpha]=.843), example items include "I love the fact I am Maori" and "Being Maori is NOT important to who I am as a person" (reverse coded). The Cultural Efficacy and Active Identity Engagement (CEAIE) subscale also used eight items ([alpha]=.858), including "I can't do Maori cultural stuff properly" (reverse coded). The subscale for Interdependent Self-Concept used seven items ([alpha]=.810) including "My Maori identity is fundamentally about my relationships with other Maori" and "My relationships with other Maori people (friends and family) are what make me Maori". Spirituality was assessed using eight items ([alpha]=.810), for example "I feel a strong spiritual association with the land" and "I don't believe in that Maori spiritual stuff" (reverse coded). We looked at Socio-Political Consciousness by using eight items ([alpha]=.882) including the items "I stand up for Maori rights" and "Maori would be heaps better off if they just forgot about the past and moved on" (reverse coded). Authenticity Beliefs were assessed by using the eight item scale ([alpha]=.603) including items like "You can tell a true Maori just by looking at them" and "Real Maori put their whanau first". The final dimension, Perceived Appearance was assessed with seven items ([alpha]=.918), examples include: "You only need to look at me to see that I am Maori".

Analytic Approach

We conducted four separate Multigroup Confirmatory Factor Analyses (MCFA), assessing the configural, metric, and scalar equivalence of the MMM-ICE2 for Maori across different demographic factors. The four demographic factors we examined were:

(a) Urban Maori versus rural Maori.

(b) Women and men.

(c) Broad age cohorts (40 years and under, 41-54 years, and 55 years and over).

(d) Sole-identified Maori versus Maori who identify with a least one other ethnic group.

We estimated these models using Maximum Likelihood with Robust error estimation (MLR) using MPlus 7.3. MLR is a maximum likelihood estimator that means the standard errors and chi-square test statistic are robust to non-normality and non-independence of observations (Muthen & Muthen, 2012). For each demographic, we first conducted standard CFAs separately for each subgroup (e.g., separate CFAs of the MMM-ICE2 for Maori men, and another for Maori women), and then a MCFA assessing the configural, metric and scalar equivalent of the MMM-ICE2 in a model directly comparing these groups (e.g., a MCFA comparing the solution for Maori men and women).


Table 2 presents fit indices for CFAs assessing each group within each model is examined independently (e.g., a model for men, a model for women), and also the configural, metric, and scalar tests for each model directly comparing groups (e.g., comparing men and women). We present the results for both the independent CFAs and MCFA for the purposes of completeness, so that interested readers have information that can inform their use of the scale both in a specific population of Maori (e.g., Maori men, or Maori of a certain age), as well as the equivalence of the scale access different demographic groups.

For interpretation of model fit we present measures of exact fit: model [chi square], and indicators of relative fit: the TuckerLewis Index (TLI), the Comparative Fit Index (CFI), the Root Mean Squared Error of Approximation (RMSEA), and the Standardised Root Mean Square Residual (SRMR). We present a variety of indices of relative fit as model [chi square] alone is not an appropriate assessment of model fit, and recommendations advocate the presentation of a range of fit indices (Bentler, 2007). This is because [chi square] is an indicator of exact fit: one's test is either significant (the model does not fit) or not (the model does fit) and because we have sample sizes over 200 [chi square] will always be significant (Barrett, 2007). Due to this limitation we additionally present indicators of relative fit: the TLI, CFI, RMSEA, and SRMR. Relative fit measures tell the researcher not whether the model fits exactly, but whether the level of fit in a model is acceptable.

However, finding an exact cut-off value for relative model fit is difficult (as it depends on a number of factors; Hu & Bentler, 1998; Marsh, Hau, & Wen, 2004) and well-contested (and perhaps in contrast to the point of "relative" fit; Barrett, 2007; Bentler, 2007; Hayduk, Cummings, Boadu, Pazderka-Robinson, & Boulianne, 2007; Marsh et al., 2004). Standard guidelines or 'rules-of-thumb' generally recommend that an RMSEA of less than .08 indicates acceptable model fit and an RMSEA of less than .05 indicates excellent fit (Marsh et al., 2004). For SRMR, Hu and Bentler (1999) have reported a standard 'rule-of-thumb' of less than .08 is generally desirable. They also propose that CFI and TLI should be greater than .95, but a CFI and TLI greater than .90 may also indicate a reasonable model.

As can be seen in Table 2, the overall CFA model provided reasonable fit across the whole sample ([chi square](1356, N=678)=5004.69, p<.001, TLI=.795, CFI=.806, RMSEA=.063, SRMR =.074). Additionally, the independent CFAs for each group across each test also indicated that the MMM-ICE2 fits reasonably well when examining each group independently. The configural models for the MCFAs for region ([chi square](2712, N=675)=6307.43, p<.001, TLI=.770, CFI=.782, RMSEA=.063, SRMR =.080), gender [chi square](2712, N=678)=6110.77, p<.001, TLI=.784, CFI=.796, RMSEA=.061, SRMR =.079), age groups ([chi square](4068, N=677)=8067.16, p<.001, TLI=.760, CFI=.772, RMSEA=.066, SRMR =.085), and sole versus mixed Maori ([chi square](2712, N=678)=6045.70, p<.001, TLI=.767, CFI=.779, RMSEA=.060, SRMR =.086) performed reasonably well. Although, the SRMR for both the age groups and ethnicity models was above the .08 generally recommended for acceptable fit. The TLI and CFI were also below the recommended .90 cut-off.

Additionally presented in Table 2 are the results for the metric models. Metric equivalence is attained if the factor loadings are the same across groups. The results for the metric models are as follows: for region ([chi square] (2759, N=675)=6328.04, p <.001, TLI=. 776, CFI = 784, RMSEA=.062, SRMR =.081), gender ([chi square](2759, N=678)=6167.88, p<.001, TLI=.787, CFI=.795, RMSEA=.060, SRMR =.081), age groups ([chi square](4162, N=677)=8179.29, p<.001, TLI=.764, CFI=.771, RMSEA=.065, SRMR =.087), and sole versus mixed Maori ([chi square](2759, N=678)=6208.25, p<.001, TLI=.763, CFI=.771, RMSEA=.061, SRMR =.088). Again, no models had a TLI or CFI higher than the .90 cut-off value. Additionally, the SRMR for the age and ethnicity models were again well above .08.

The results for our third and most stringent test of the measurement equivalence of the MMM-ICE2 are also presented in Table 2. Recall that scalar equivalence assesses the similarity of the intercepts for each item across groups. The results for the scalar models are as follows: for region ([chi square](2806, N=675)=6383.69, p <.001, TLI = .779, CFI = .784, RMSEA=.061, SRMR=.081), gender ([chi square](2806, N=678)=6304.97, p<.001, TLI=.786, CFI=.790, RMSEA=.061, SRMR =.082), age groups ([chi square](4256, N=677)=8438.86, p<.001, TLI=.760, CFI=.762, RMSEA=.066, SRMR =.088), and sole versus mixed Maori ([chi square](2806, N=678)=6366.07, p<.001, TLI=.759, CFI=.764, RMSEA=.061, SRMR=.090). As with the configural and metric models, the scalar models for ethnicity and age had SRMR values higher than the desired .08. Again, the TLI and CFI values for each model were lower than the desired .90.

We then tested for differences in model fit for each group comparison using chi-square difference tests and change in CFI. When assessing model fit we assessed the metric against the configural model, then the scalar against the configural model. We conducted chi-square difference tests. In these tests if the more restrictive model (e.g. scalar), is significantly different from the less restrictive one (e.g. metric), then the model does not fit as well. Additionally, Cheung and Rensvold (2002) propose that fit can be assessed incrementally with change in CFI across these models: if [DELTA]CFI is less than .01 the more restrictive model can be accepted.

For region, the metric against configural model ([DELTA][chi square](47)=28.17, p=.987; [DELTA]CFI=.002), the scalar against configural model ([DELTA][chi square](94)=76.43, p=.907; [DELTA]CFI=.002), and the scalar against metric model ([DELTA][chi square](47)=50.33, p=.343; [DELTA]CFI=.000) did not significantly differ in fit and [DELTA]CFI was below the <.01 threshold. For gender, the metric and configural model did not significantly differ in fit ([DELTA][chi square](47)=59.37, p=.106; [DELTA]CFI=.001). The scalar and configural model ([DELTA][chi square](94)= 193.77, p <.001; [DELTA]CFI=.006), and the scalar against the metric model ([DELTA][chi square](47)=140.60, p<.001; [DELTA]CFI=.005) results indicated that the more restrictive measurement equivalence models did not fit as well as the metric model. However, when assessing [DELTA]CFI, the differences were below .01, indicating that the more restrictive models can be accepted in both cases.

We found when testing both age cohort and sole versus mixed Maori, the more restrictive models significantly differed from the fit of the less restrictive metric models. For the age cohorts there were significant differences for the metric against configural ([DELTA][chi square](94)=120.32, p=.035; [DELTA]CFI=.001), scalar and configural ([DELTA][chi square](188)= 371.73, p<.001; [DELTA]CFI=.010), and the scalar against metric models ([DELTA][chi square](94)=264.28, p<.001; [DELTA]CFI=.009). However, the [DELTA]CFI for each comparison came in equal to or below the <.01 guideline indicating that the more restrictive models can be accepted in this case, although [DELTA]CFI for the configural versus scalar comparison was .01.

The results were similar for sole versus mixed Maori. There were significant differences for the metric against configural models ([DELTA][chi square](47)=155.07, p<.001; [DELTA]CFI=.008), the scalar and configural models ([DELTA][chi square](94)= 316.10, p<.001; [DELTA]CFI=.015), and the scalar against metric models ([DELTA][chi square](47)=161.76, p<.001; [DELTA]CFI=.008). However, when using [DELTA]CFI as an indicator of model fit, the metric versus configural and configural versus scalar models were under the <.01 guideline. The threshold of [DELTA]CFI <.01 was not met when comparing the configural model to the most restrictive scalar model, with the change being .015.


The MMM-ICE2 is a scale that purports to measure subjective Maori ethnic identity in a scale specific to Maori. However, Maori are a diverse group, which may present problems for any scale wishing to capture the multiplicity of Maori identity (Durie, 1994; Greaves et al., 2015). Thus, we aimed to answer the questions: does the MMM-ICE2 measure the same concepts across all Maori? Even across such diverse groups as urban Maori, rural Maori, Maori men, Maori women, young Maori, older Maori, those solely-identified as Maori, and bi-/multi-ethnic identifying Maori? As such, we conducted several Multigroup Confirmatory Factor Analyses to test measurement equivalence across these groups.

Our results showed that the scale performed well across region (urban or rural) and gender (female or male), the only exception being that the region and gender models did not reach the .90 guideline for TLI or CFI at any point. However, it bears keeping in mind that TLI and CFI may have been sensitive to the large number of items on the scale (Cheung & Rensvold, 2002). The ethnicity (sole or mixed identifying Maori) and age (40 and under, 41-54, and 55 plus) models again did not meet the .90 recommended for TLI or CFI, and had an SRMR higher than the recommended .80. Additionally, when comparing the configural (base) model and the most conservative scalar models, the results were just over the guideline for ethnicity and right on the rule-of-thumb value for age. This indicates two areas where the scale could have performed better. Our results suggest that the intercepts for the indicators are not similar across these groups. When examining the CFA results, the key weaker areas for the MMM-ICE2 was the comparison between older Maori and sole identifying Maori, and the comparison between age groups.

To put this in practical terms, those who are older (when compared to the younger age groups), or those who vary across ethnic affiliation, may have conceptually the same level of identification with a MMM-ICE2 domain, but a different mean score on an item across groups. For example, across age groups people may conceptually, equally agree with the item "Being Maori is cool" however, they may have a different mean score on this item due to a variety of possible reasons. The result is that any mean differences found across groups, across items, may not be related to there being a real difference in scores.

Therefore, if someone were to conduct research exploring age differences or differences between sole-and mixed-Maori in a domain of the MMM-ICE2, there is a possibility some of the differences found could be attributed to measurement invariance. However, in both cases these comparisons fell barely short of the guideline we used for model fit (change in CFI). Additionally, in future, those working with the MMM-ICE2 should also try to replicate our results in an independent sample of Maori as intercepts, and therefore scalar invariance, may be sample-specific (Vandenberg & Lance, 2000). Generally, the results of our analyses should provide confidence to researchers that the MMM-ICE2 can continue to be used as a scale to measure Maori identity across broad and diverse samples of Maori.

It is also important to keep in mind that the Maori population is youthful compared to the non-Maori population (Statistics New Zealand, 2013). As such representative samples of Maori tend to have lower rates of people over 55 (or older: only around 5% of the Maori population is over 65; Statistics New Zealand, 2013) compared to samples of the general population. Further, younger people may be more familiar with the format and goals of surveys. It could be interesting to test measurement equivalence with a sample of Maori over time (Vandenberg & Lance, 2000) to explore whether the slight measurement invariance we found here is a cohort effect, i.e. whether it is due to a feature of this cohort of older Maori, or whether these effects for equivalence change as people age. Additionally, future studies examining the scale properties of the MMM-ICE2 could explore the particular items that were invariant (Byrne, Shavelson, & Muthen, 1989).

There remains the possibility that a couple of key things are missing from this examination of the MMM-ICE2 scale, and this sample used to test the MMM-ICE2 more generally. While the MMM-ICE2 purports to be a scale of Maori identity, there is the possibility that some unexamined part of Maori identity is not measured in the scale. This would mean that the scale is not a complete picture of Maori identity and can be remedied with improvements and feedback over time (like the addition of the Perceived Appearance dimension in the MMM-ICE2; Houkamau & Sibley, 2015a). Another limitation is the relatively low response rate to the survey (7.78% when electoral roll address accuracy adjusted). Participants were opting into a 16 year longitudinal survey and this may have been off-putting. However, survey response rates have been dropping over time and the effect is particularly pronounced for Maori (see Fink, Paine, Gander, Harris, & Purdie, 2011; Sibley 2014). This low response rate may mean that the sample tested here was biased in some way.

One problem is that we cannot know if our sample differs in views or identity to non-respondents, although, the sample look reasonably representative compared with census data on the Maori population (notwithstanding gender; Sibley, Muriwai, & Greaves, 2014). However, it may be that there is a group of Maori who are resistant to surveys, a Western concept that they may view as being linked to the Government. Additionally the survey was only sent in English and not te reo Maori. This may be the case, considering that the model did not fit as well for sole-identifying and older Maori, groups who may speak te reo. Alternatively, there may have been problems with address accuracy--it may be that some aspect of Maori identity predicts moving house more often and we have missed an important group--or we may have missed a group of more economically deprived Maori. However, these are all speculative, and we hope to follow up on these ideas with future analyses.

A key future research direction for the MMM-ICE2, however, is to collect longitudinal data. There are plans for a follow up Maori focus questionnaire in the next couple of years. This means that more complex, longitudinal models can be created to help us better understand how Maori identity may change over time. There is currently a need for research to discover how Maori identity may change with age, although extant research suggests that Maori may become more enculturated as they get older (Sibley & Houkamau, 2013; Greaves et al., 2015). Furthermore, collecting data from adolescent Maori, to both compare age groups and to examine scores as they age, are potential future research directions. Here, we have found that the intercepts of the scale may vary by age, meaning that future research examining age and Maori identity will need to examine, and control for, measurement invariance. We hope that the groundwork laid in this paper allows for future longitudinal research to be conducted with relative confidence that the MMM-ICE2 is an efficacious measure of the broad, diverse group that are 'Maori'.


This manuscript is based on part of Lara Greaves' PhD thesis supervised by Chris Sibley and Carla Houkamau. Lara Greaves was supported by a University of Auckland Doctoral Scholarship during the preparation of this manuscript. This research was supported by a Te Whare Kura New Knowledge Acquisition Grant awarded to Carla Houkamau and Chris Sibley (#03903/1550). Data collection for the NZAVS was also supported by a Templeton World Charity Foundation Grant (ID: 0077). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. As per the NZAVS data access statement, a copy of the anonymous data reported in each NZAVS publication is available from CS upon request from appropriately qualified researchers. Such data will be provided with the explicit understanding that it is used solely for the purposes of replicating or otherwise checking the validity of analyses reported in scientific papers analyzing NZAVS data.


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Lara M. Greaves (1), Sam Manuela (1), Emerald Muriwai (2), Lucy J. Cowie (1), Cinnamon-Jo Lindsay (1), Correna M. Matika (1) Carla A. Houkamau (1) & Chris G. Sibley (1)

(1) University of Auckland, (2) SHORE & Whariki Research Centre, Massey University, Auckland,

Corresponding Author:

Lara M. Greaves

School of Psychology,

University of Auckland,

Private Bag 92019,

Auckland 1142,

New Zealand


Table A1.
Item content for the MMM-ICE2 by dimension.

Group Membership Evaluation (GME)

1.    I reckon being Maori is awesome.
2.    I love the fact I am Maori.
3.    Being Maori is cool.
4.    I don't really care about following Maori culture.
5.    I wish I could hide the fact that I am Maori from other
6.    My Maori ancestry is important to me.
7.    Being Maori is NOT important to who I am as a person.
8.    Being Maori is NOT important to my sense of what kind of
        person I am.

Cultural Efficacy and Active Identity Engagement (CEAIE)

9.    I don't know how to act like a real Maori on a marae.
10.   I can't do Maori cultural stuff properly.
11.   I can't do Maori culture or speak Maori.
12.   I know how to act the right way when I am on a marae.
13.   I'm comfortable doing Maori cultural stuff when I need to.
14.   I have a clear sense of my Maori heritage and what it means
        for me.
15.   I try to korero (speak) Maori whenever I can.
16.   I sometimes feel that I don't fit in with other Maori.

Interdependent Self-Concept (ISC)

17.   My relationships with other Maori people (friends and
        family) are what make me Maori.
18.   I consider myself Maori because I am interconnected with
        other Maori people, including friends and family.
19.   My Maori identity is fundamentally about my relationships
        with other Maori.
20.   For me, a big part of being Maori is my relationships with
        other Maori people.
21.   How I see myself is totally tied up with my relationships
        with my Maori friends and family.
22.   My Maori identity belongs to me personally. It has nothing
        to do with my relationships with other Maori.
23.   Reciprocity (give-and-take) is at the heart of what it
        means to be Maori for me.

Spirituality (S)

24.   I believe that Tupuna (ancient ancestors) can communicate
        with you if they want to.
25.   I don't believe in that Maori spiritual stuff.
26.   I believe that my Taha Wairua (my spiritual side) is an
        important part of my Maori identity.
27.   I can sense it when I am in a Tapu place.
28.   I can sometimes feel my Maori ancestors watching over me.
29.   I have never felt a spiritual connection with my ancestors.
30.   I think Tapu is just a made up thing. It can't actually
        affect you.
31.   I feel a strong spiritual association with the land.

Socio-Political Consciousness (SPC)

1.    Maori would be heaps better off if they just forgot about
        the past and moved on.
2.    All of us, both Maori and Pakeha, did bad things in the
        past--we should all just forget about it.
3.    I'm sick of hearing about the Treaty of Waitangi and how
        Maori had their land stolen.
4.    I think we should all just be New Zealanders and forget
        about differences between Maori and Pakeha.
5.    I think that Maori have been wronged in the past, and that
        we should stand up for what is ours.
6.    What the European settlers did to Maori in the past has
        nothing to do with me personally. I wasn't there and I
        don't think it affects me at all.
7.    I stand up for Maori rights.
8.    It's important for Maori to stand together and be strong
        if we want to claim back the lands that were taken from

Authenticity Beliefs (AB)

9.    You can always tell true Maori from other Maori. They're
        real different.
10.   I reckon that true Maori hang out at their marae all
        the time.
11.   True Maori always do karakia (prayer) before important
12.   You can tell a true Maori just by looking at them.
13.   Real Maori put their whanau first.
14.   To be truly Maori you need to understand your whakapapa
        and the history of your people.
15.   You can be a real Maori even if you don't know your Iwi.
16.   You can be a true Maori without ever speaking Maori.

Perceived Appearance (PA)

17.   I think it is easy to tell that I am Maori just by looking
        at me.
18.   You only need to look at me to see that I am Maori.
19.   When people meet me, they often do not realize that I am
20.   I think it is hard to tell that I am Maori just by looking
        at me.
21.   I think it is clear to other people when they look at me
        that I am of Maori descent.
22.   People would never know that I am of Maori descent just by
        looking at me.
23.   People who don't know me often assume that I am from
        another (non-Maori) ethnic group.

Table 1

Construct definitions for the seven factors indexed by the
MMM-ICE2. Adapted from Houkamau and Sibley (2015a).

Group Membership Evaluation (GME)

The extent to which the individual positively evaluates their
  membership in the social category Maori and views their
  membership as Maori as a personally important or central aspect
  of their self-concept versus the extent to which the individual
  negatively evaluates their membership in the social category
  Maori and views their membership as Maori as peripheral or
  irrelevant to their self-concept

Cultural Efficacy and Active Identity Engagement (CEAIE)

The extent to which the individual perceives that they have the
  personal resources required (i.e., the personal efficacy) to
  engage appropriately with other Maori in Maori social and
  cultural contexts versus the extent to which the individual
  perceives that they lack the personal resources and ability to
  engage appropriately with other Maori in Maori social and
  cultural contexts

Interdependent Self-Concept (ISC)

The extent to which the concept of the self-as-Maori is defined by
  virtue of relationships with other Maori people versus the extent
  to which the concept of the self-as-Maori is viewed as being
  defined as solely unique and independent to the individual rather
  than as part of the social group.

Spirituality (S)

The extent to which the individual is engaged with, and has a
  belief in, certain Maori concepts of spirituality, including a
  strong connection with ancestors, Maori traditions, the sensation
  and experience of waahi tapu (sacred places), and a strong
  spiritual attachment and feeling of connectedness with the land
  versus the extent to which the individual is disengaged from or
  does not believe in Maori concepts of spirituality.

Socio-Political Consciousness (SPC)

The extent to which the individual perceives historical factors as
  being of continued importance for understanding contemporary
  intergroup relations between Maori and other ethnic groups in New
  Zealand; and how actively engaged the individual is in promoting
  and defending Maori rights given the context of the Treaty of
  Waitangi versus the extent to which the individual perceives
  historical factors and injustices experienced by Maori as being
  irrelevant in contemporary society.

Authenticity Beliefs (AB)

The extent to which the individual believes that to be a 'real' or
  'authentic' member of the social category Maori one must display
  specific (stereotypical) features, knowledge and behaviour versus
  the extent to which the individual believes that Maori identity
  is fluid rather than fixed, and produced through lived

Perceived Appearance (PA)

The extent to which people subjectively evaluate their appearance
  as having clear and visible features that signalling their
  ethnicity and ancestry as Maori (or high Maori prototypicality)
  versus the extent to which people evaluate their appearance as
  less indicative of having Maori ancestry (low Maori

Table 2

Fit indices for Standard and Multigroup CFAs assessing the
equivalence of the MMM-ICE2 across different groups.

                   N     [chi      df    TLI    CFI    RMSEA   SRMR

Standard CFAs

Overall model     678   5004.69   1356   .795   .806   .063    .074
  Urban           315   3543.51   1356   .744   .757   .072    .087
  Rural           360   3365.38   1356   .791   .802   .064    .074
Gender Models
  Women           428   2920.27   1356   .765   .777   .066    .083
  Men             250   2772.51   1356   .807   .818   .065    .072
Age Models
  40 and under    271   2908.74   1356   .807   .817   .065    .075
  41-54           186   2670.49   1356   .739   .753   .072    .088
  55+             221   2695.81   1356   .714   .729   .073    .095
  Sole            305   3453.95   1356   .672   .689   .071    .104
  Mixed           373   3166.15   1356   .823   .832   .060    .067

Multigroup CFA
Regional Model

Configural        675   6307.43   2712   .770   .782   .063    .080
Metric model            6328.04   2759   .776   .784   .062    .081
Scalar model            6383.69   2806   .779   .784   .061    .081

Gender Model      678   6110.77   2712   .784   .796   .061    .079

Metric model            6167.88   2759   .787   .795   .060    .081
Scalar model            6304.97   2806   .786   .790   .061    .082

Age Model

Configural        677   8067.16   4068   .760   .772   .066    .085
Metric model            8179.29   4162   .764   .771   .065    .087
Scalar model            8438.86   4256   .760   .762   .066    .088

Ethnicity Model

Configural        678   6045.70   2712   .767   .779   .060    .086
Metric model            6208.25   2759   .763   .771   .061    .088
Scalar model            6366.07   2806   .759   .764   .061    .090
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Author:Greaves, Lara M.; Manuela, Sam; Muriwai, Emerald; Cowie, Lucy J.; Lindsay, Cinnamon-Jo; Matika, Corr
Publication:New Zealand Journal of Psychology
Article Type:Report
Date:Apr 1, 2017
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