title: Weaving an interpretivist stance throughout mixed methods research

authors: McChesney, Katrina

subjects: Mixed methods research

abstract: A recurring debate in mixed methods research involves the relationship between research methods and research paradigms. Whereas some scholars appear to assume that qualitative and quantitative research methods each necessarily belong with particular research paradigms, others have called for greater flexibility and have taken a variety of stances toward the integration of paradigms and methods in mixed-method studies. In this article, we review these arguments and stances, positioning ourselves in favour of flexible (but intentional) integration of any research method with any research paradigm. We then draw on a recent study of teachers’ experiences of professional development to provide an illustration of how a single paradigm can be used to inform the entirety of a mixed methods study, including study design, data collection, analysis and reporting. This illustration is particularly noteworthy since past mixed-method studies that have been grounded in a single paradigm have typically used the post-positivist paradigm, whereas our study involved an interpretive stance and a social constructivist epistemology. This article may, therefore, provide a useful resource for those considering the design of mixed methods studies as well as a practical demonstration to support theoretical claims in support of moving away from binary methods–paradigm associations and assumptions.

text: Weaving an interpretivist stance throughout mixed methods research A recurring debate in mixed methods research involves the relationship between research methods and research paradigms. Whereas some scholars appear to assume that qualitative and quantitative research methods each necessarily belong with particular research paradigms, others have called for greater flexibility and have taken a variety of stances toward the integration of paradigms and methods in mixed-method studies. In this article, we review these arguments and stances, positioning ourselves in favour of flexible (but intentional) integration of any research method with any research paradigm. We then draw on a recent study of teachers’ experiences of professional development to provide an illustration of how a single paradigm can be used to inform the entirety of a mixed methods study, including study design, data collection, analysis and reporting. This illustration is particularly noteworthy since past mixed-method studies that have been grounded in a single paradigm have typically used the post-positivist paradigm, whereas our study involved an interpretive stance and a social constructivist epistemology. This article may, therefore, provide a useful resource for those considering the design of mixed methods studies as well as a practical demonstration to support theoretical claims in support of moving away from binary methods–paradigm associations and assumptions.

year: 2019

title: Computational Bayesian inference using low discrepancy sequences

authors: Brown, Paul Tamataatoi

subjects: Bayesian Inference

abstract: The Integrated Nested Laplace Approximation (INLA) provides fast and accurate Bayesian inference for complex hierarchical models. For INLA, and other deterministic methods, the hyperparameter space is explored and points are laid out in a grid structure. These points are used in some numerical integration scheme for which marginal posterior distributions are computed. The main drawback is that the number of points increase exponentially with the number of hyperparameters. The grid is a type of quasi-Monte Carlo (QMC) point set. Low discrepancy sequences (LDS) are QMC point sets that are well known to have significant advantages over grids in terms of convergence and accuracy, and suffer less from the so-called curse of dimensionality.

This work makes several important contributions. We introduce a new method using LDS to compute marginal posterior distributions for hyperparameters, discuss the convergence properties of the approximations and show that they converge to the true posterior. We also show how these methods can be incorporated into the INLA inference framework, and we outline important extensions that improve the accuracy of our approximations with little extra computational effort needed. Lastly, we build a unique spatio-temporal model of residential crime in Hamilton, using INLA’s stochastic partial differential equation approach to a Log-Gaussian Cox Process, and use an LDS to approximate the latent parameters of the model.

Our results show that for a fixed number of points or computational time, LDS methods can outperform general grid-based methods, leading to better marginal posterior approximations. Modifying the method for the purposes of incorporation to INLA, we show that we can outperform INLA’s grid with respect to computational speed, and obtain accurate and flexible approximations to the model hyperparameters.

text: Computational Bayesian inference using low discrepancy sequences The Integrated Nested Laplace Approximation (INLA) provides fast and accurate Bayesian inference for complex hierarchical models. For INLA, and other deterministic methods, the hyperparameter space is explored and points are laid out in a grid structure. These points are used in some numerical integration scheme for which marginal posterior distributions are computed. The main drawback is that the number of points increase exponentially with the number of hyperparameters. The grid is a type of quasi-Monte Carlo (QMC) point set. Low discrepancy sequences (LDS) are QMC point sets that are well known to have significant advantages over grids in terms of convergence and accuracy, and suffer less from the so-called curse of dimensionality.

This work makes several important contributions. We introduce a new method using LDS to compute marginal posterior distributions for hyperparameters, discuss the convergence properties of the approximations and show that they converge to the true posterior. We also show how these methods can be incorporated into the INLA inference framework, and we outline important extensions that improve the accuracy of our approximations with little extra computational effort needed. Lastly, we build a unique spatio-temporal model of residential crime in Hamilton, using INLA’s stochastic partial differential equation approach to a Log-Gaussian Cox Process, and use an LDS to approximate the latent parameters of the model.

Our results show that for a fixed number of points or computational time, LDS methods can outperform general grid-based methods, leading to better marginal posterior approximations. Modifying the method for the purposes of incorporation to INLA, we show that we can outperform INLA’s grid with respect to computational speed, and obtain accurate and flexible approximations to the model hyperparameters.

year: 2019

title: Virtual hākari:  Sharing Māori culinary traditions in online communities

authors: Muru-Lanning, Charlotte

subjects: Kai Māori

abstract: For Māori, kai is a vital expression of identity, community, place and whakapapa. Traditionally, knowledge about kai is transmitted through customary community groupings and culturally embedded practices. However, with the rise of digital platforms, new spaces have emerged for Māori to gather and to share kai in virtual forms. 
This thesis observes how two Facebook groups – Kai Maori and KAI Basket NZ – operate as contemporary spaces for the transmission of Māori culinary knowledge and cultural identity. Kai Māori is considered alongside global studies of culinary traditions and understood through the notion of kai as whakapapa. The thesis addresses two core research questions: 1) How do Facebook groups contribute to an evolving concept of kai Māori? and 2) What kinds of relationships define these online kai communities? 
Guided by Māori data sovereignty (MDSov) principles, I observed interactions on both Facebook pages in two phases – one involving selective data collection over a twelve-month period from January to December 2024 the other involving systematic data collection over a four-week period from 10 December 2024 to 10 January 2025. The observation periods yielded 115 and 1293 posts respectively. A covert digital approach of ‘lurking’ was adopted as seeking prior consent may have affected the quality of the data and disrupted group dynamics. Lurking, as a method, sits uneasily alongside MDSov principles, particularly the principle of manaakitanga, requiring free, prior and informed consent. To address this I safeguarded the confidentiality of community members by seeking consent before reproducing content, removing group members’ names and excluding sensitive information. To analyse posts I used Ethnographic Content Analysis which allowed me to conduct a reflexive, iterative analysis of the posts in a way that was sensitive to the context in which the content was created.
These digital observations show that these groups serve as platforms for the transmission and innovation of kai Māori, encompassing edible components as well as the values enmeshed within these culinary traditions. Despite the mediated nature of these exchanges – where food is virtually consumed rather than physically shared, separate from traditional notions of community – these groups nurture meaningful connections among members, including those physically distant from their whenua. Through recipes, photos, stories, and commentary, the members of Kai Maori and KAI Basket NZ cultivate community identity and belonging via common cultural understandings, sharing of knowledge, a general spirit of sociality – and, importantly, a mutual love of kai.
I conceptualise these online spaces as virtual hākari, where the act of sharing virtual kai becomes an affirmation of identity and a form of cultural resistance. While online sharing may risk distancing kai practices and knowledge from traditional sites of transmission, the data suggests that these platforms may serve as conduits that encourage deeper cultural engagement offline. This thesis highlights the centrality of food in Māori cultural survival, sovereignty and resistance. In these digital spaces, kai Māori is not only celebrated but continually reimagined – reinforcing that to prepare, share and celebrate kai as Māori is to actively participate in the continuity of cultural identity.

text: Virtual hākari:  Sharing Māori culinary traditions in online communities For Māori, kai is a vital expression of identity, community, place and whakapapa. Traditionally, knowledge about kai is transmitted through customary community groupings and culturally embedded practices. However, with the rise of digital platforms, new spaces have emerged for Māori to gather and to share kai in virtual forms. 
This thesis observes how two Facebook groups – Kai Maori and KAI Basket NZ – operate as contemporary spaces for the transmission of Māori culinary knowledge and cultural identity. Kai Māori is considered alongside global studies of culinary traditions and understood through the notion of kai as whakapapa. The thesis addresses two core research questions: 1) How do Facebook groups contribute to an evolving concept of kai Māori? and 2) What kinds of relationships define these online kai communities? 
Guided by Māori data sovereignty (MDSov) principles, I observed interactions on both Facebook pages in two phases – one involving selective data collection over a twelve-month period from January to December 2024 the other involving systematic data collection over a four-week period from 10 December 2024 to 10 January 2025. The observation periods yielded 115 and 1293 posts respectively. A covert digital approach of ‘lurking’ was adopted as seeking prior consent may have affected the quality of the data and disrupted group dynamics. Lurking, as a method, sits uneasily alongside MDSov principles, particularly the principle of manaakitanga, requiring free, prior and informed consent. To address this I safeguarded the confidentiality of community members by seeking consent before reproducing content, removing group members’ names and excluding sensitive information. To analyse posts I used Ethnographic Content Analysis which allowed me to conduct a reflexive, iterative analysis of the posts in a way that was sensitive to the context in which the content was created.
These digital observations show that these groups serve as platforms for the transmission and innovation of kai Māori, encompassing edible components as well as the values enmeshed within these culinary traditions. Despite the mediated nature of these exchanges – where food is virtually consumed rather than physically shared, separate from traditional notions of community – these groups nurture meaningful connections among members, including those physically distant from their whenua. Through recipes, photos, stories, and commentary, the members of Kai Maori and KAI Basket NZ cultivate community identity and belonging via common cultural understandings, sharing of knowledge, a general spirit of sociality – and, importantly, a mutual love of kai.
I conceptualise these online spaces as virtual hākari, where the act of sharing virtual kai becomes an affirmation of identity and a form of cultural resistance. While online sharing may risk distancing kai practices and knowledge from traditional sites of transmission, the data suggests that these platforms may serve as conduits that encourage deeper cultural engagement offline. This thesis highlights the centrality of food in Māori cultural survival, sovereignty and resistance. In these digital spaces, kai Māori is not only celebrated but continually reimagined – reinforcing that to prepare, share and celebrate kai as Māori is to actively participate in the continuity of cultural identity.

year: 2025