According to Creswell (2003), there are six types of mixed method research design: 1) sequential explanatory; 2) sequential exploratory; 3) sequential transformative; 4) concurrent triangulation; 5) concurrent nested; and 6) concurrent transformative.
Creswell has a number of different lists of how many mixed methods designs there are. I personally prefer a more systematic approach to defining those designs, which you will find in my book: "Integrating Qualitative and Quantitative Methods" from Sage.
Briefly, I would distinguish convergent comparisons (concurrent triangulation) from designs that combine qualitative and quantitative methods without comparing them (no real equivalent in the Creswell list above). And I would distinguish both of those designs from sequential designs, including both the designs with dominant quantitative methods (sequential exploratory and sequential explanatory) and two further sequential designs that are qualitatively driven.
I don't consider nested designs to be a separate category, because they simply involve including a qualitative study within a predominantly quantitative study, and most of them turn out to be sequential explanatory designs (i.e., explaining portions of the quantitative results using further qualitative data).
As far as I know, Creswell has pretty much dropped sequential transformative and concurrent transformative designs from his later lists.
I still find Creswell's six types of mixed method research design relevant depending on the type of study to be conducted. However, the sequential explanatory, sequential exploratory lend themselves easily to whether you want to start with either qualitative or quantitative as majority of people were more inclined to use what was previously referred to as combination of methods. At the same time, for gender and feminist related studies, transformative designs, more relevant designs.
Useful discussion - I find Schifferdecker and Reed's paper useful for mixed methods designs (https://www.ncbi.nlm.nih.gov/pubmed/19573186). Would anyone expand on transformative study designs - I have found different explanations for it in different papers and books.
Summarizing the perspectives of several authors, I would say that there are 3 main types of mixed methods designs:
1) Concurrent design (triangulation): The qualitative and quantitative components are deployed simultaneously and their results are compared.
2) Exploratory sequential design. The qualitative study goes first and is the main one. From it, hypotheses are generated or instruments are developed. The second phase is the deployment of the quantitative component.
3) Confirmatory sequence design. The quantitative study unfolds first and is the main one. Subsequently the qualitative study is performed to better understand the quantitative results obtained.
I would add two additional elements to Jorge Cruz-Cárdenas' summary.
1. There are concurrent designs that do not involve triangulation in the sense of a direct comparison to two studies on the same research topic. Instead, each method can add something to the other. Unfortunately, there is no consensus on the name for such designs, but in my work I call then "additional coverage," and they can be represented as QUAL + quant and QUANT + qual.
2. The exploratory sequential design (qual --> QUANT) and explanatory sequential design (QUANT -->qual) are both quantitatively driven, but lately there has been considerable interest in the alternative of qualitatively driven designs (QUAL --> quant and quant --> QUAL), although these two designs also do not have any widely accepted names.
I recommend intensively mixed method with multiple combinations and sequences of quantitative and qualitative methods. More details can be seen in my paper on Flexible Systems Methodology.
I agree that Creswell has changed the list of types of research design over time, apparently in an attempt to address different disciplinary, paradym or contextual drivers. A useful resource is his 2013 paper/presentation Steps in Conducting a Scholarly Mixed Methods Study available at https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1047&context=dberspeakers
As well as providing an excellent outline of the steps in mixed method research design , it also provides a flow charts of 3 basic and 3 advanced methods
Mixed-methods approach has received more than it deserves. The more you read the more you get confused. Scholars do not agree on a specific number of types of mixed methods design. I started reading about mixed-methods in 2006, I have come across 4 types, 6 types and 12 types. This is evident in the answers given above here. Tashakkori and Teddlie (2003) noted that they had found nearly 40 different types of mixed methods designs. Creswell, Plano Clark, et al. (2003) have summarized the range of these classifications in 12 types. This confusing matter can be attributed to the approach scholars adopt in their classification of these types. Further, scholars have been descriptive in their classifications; they browse published studies that used mixed-methods and generate their classification. Best thing to do is to read what has been suggested by scholars concerning the classification of mixed methods and the classification that matches your study choose it and cite the book/book chapter/article you refer to.
I have recently completed a content analysis of over 600 randomly selected articles that used mixed methods. Although I applied a coding system that was based on eight possible types of designs, over 60% of the articles relied on "complementary" designs where one method simply added something to the other. Beyond that, exploratory and explanatory sequential designs were relatively common (qual --> QUAN and QUAN --> qual).
So, despite the wide variety of typologies and the large number of possible designs that they describe, published research in mixed methods seems to rely on only a small number of approaches in practice.
I should also add the large number of studies that relied on complementarity showed discouragingly low levels of integration between the qualitative and quantitative results. So, despite all of the expert advice about how to design well-integrated studies in mixed methods research, actual practice is far behind that standard.