This “Conversation with Authors” features Scott J. Cook (SJC), Jude C. Hays (JCH), and Robert J. Franzese, Jr. (RJF), authors of the recent open access APSR article, “STADL Up! The Spatiotemporal Autoregressive Distributed Lag Model for TSCS Data Analysis.”

APSR: What inspired you to write on this topic?

JCH: We all started with time series analysis and use time series cross-sectional (TSCS) data – which has both temporal and spatial dependence. Existing literature usually deals with the two in isolation, so we were inspired by our methodological interests and the data we work with. There not being a lot out there suggested a need for something like this.

SJC: Recent political methods research shows how addressing one problem at a time can sometimes make things worse. With TSCS data, researchers tend to neglect spatial dependence. There hasn’t been much discussion of the consequences of that and why it’s important to account for both simultaneously.

RJF: And virtually everything we study involves spatial interdependence, but almost everyone either ignores it or tries quick fixes. Addressing it requires developing a spatial-weights matrix that reflects substantive considerations and captures the important parts of that interdependence. We wanted to make this easier for applied researchers. Our code automatically generates one kind of spatial weights matrix, estimates models, and provides summary statistics for the implied spatiotemporal effects. We’re generating a Stata translation of this and hope to expand functionality.

APSR: So you were trying to solve a problem you discovered in your own research?

RJF: As comparative and international political economists, we were interested in tax competition. Globalization – the word practically means that policies in some units depend on policies elsewhere, and we weren’t seeing analyses reflecting that. Instead, you’d see tax rates put on the left-hand side, and a list of explanators, including a couple of ‘globalization’ variables, on the right.  Interdependence suggests that the policies of one state should be on the left-hand side with the policies of competitors on the right. That was our initial substantive inroad: the proper way to model this process.

APSR: What were the aims of this paper?

RJF: Correlation across space can arise from common exposure, contagion, or an unmodeled process. These generate similar spatial associations, and there are also analogous temporal dependence processes that could be operating together or separately. This has implications for how our theories manifest in the outcomes we study. We wanted to help researchers estimate spatiotemporal models that allow and consider these different theoretical manifestations, and provide some back-end tools to do this.

APSR: So you had a variety of related goals.

JCH: Yes, different goals depending on the audience. We have methods goals and applied research goals. We have goals for ‘interdependence as substance’ and as a nuisance. These emerged over 20 years of work. One of my goals is to see people treat spatial dependence like temporal dependence. If you’ve got TSCS data, you’d never get published if you didn’t address time dependence. It would be great to see similar awareness, especially from people working with country-year data, of spatial dependence.

SJC: Our goals weren’t all well-established at the outset. Some informed our decision to undertake the project and became much more specific over time.

RJF: Our initial question was ‘how do temporal and spatial interdependence interact?’ – a much narrower focus. Methods papers have a common structure: here’s a problem, simulations show it’s a big problem, and substantive replications show important implications for the conclusions we draw. In a great example of peer review working well, our colleagues encouraged us to elaborate on these demonstrations with a running example, rendering them more concrete and showing how to implement our suggestions substantively. We were developing such an example (democracy and development) for a forthcoming book project (Empirical Analysis of Spatial Interdependence). This addition tremendously improved the paper, particularly its potential impact.

APSR: What kinds of scholars would be most interested in this paper?

RJF: ‘Speaking to everyone’ is part of this four-part structure for maximizing the impact of a methods project. Part one – I don’t care what you study, this is central. Part two – we’ve been getting it wrong and drawing bad conclusions. Part three – a pile of statistics. Part four – here’s the easy ‘point and click’ code. Our ‘part four’ contribution starts with the tools we offer here for scholars working with country-year data.

APSR: What was your biggest surprise while writing this paper?

SJC: Most of the surprises spoke to the subtle ways that incorporating dependence in TSCS analyses is different from TS or CS. Years of working with these data and teaching these approaches gave us a clear sense of what happens when you omit something. Having dependence in both dimensions complicates things, and our expectations weren’t always met.

RJF: These kinds of interactions were our starting point. Most methodologists learned to deal with these problems separately. But where temporal and spatial dependence are both substantial, you need to address them simultaneously. Our Figure 5, the cube of causality over time and across space, shows how the two are mutually implicated.

JCH: There’s one specific counterintuitive case we point out. Normally, if you omit a spatial lag, there’s an inflation bias in your estimates of interest if your independent variables are spatially clustered. But with a time lag in the model, omitting the spatial lag will inflate the estimated temporal dependence, thereby producing an offsetting attenuation bias in your estimates, pushing them toward zero.

APSR: How did writing for a general political science audience affect your approach?

RJF: We restated any technical assumptions or mathematical statements in a substantive sentence. We used our running example – democracy and development – to show how different arguments correspond to different ways dependence enters the model.

SJC: We recognized that things click for different people in different ways. So we have simulations, analytical derivations, illustrations, figures, and the running example – all telling the same story. The goal, with a mixed audience, is for people to see the nuance while still getting the takeaways.

JCH: We’re working on developing code for multiple audiences, too. The first version assumes no experience with spatial dependence. All it requires is specifying a variable that identifies the nation-state and another that identifies the year.  That allows for a test of the null hypothesis of no spatial dependence.

RJF: There’s nothing in the existing literature that would help someone who didn’t already have a matrix of spatial connections among their units (or know how to create one).  Nothing for that person saying ‘I estimated an OLS regression and want to check for spatial interdependence’. Having a tool researchers can implement quickly, powerfully, and effectively in most cases, without prior familiarity with spatial analysis, is a step forward.

APSR: So, not just saying ‘do this’, but providing support in doing so?

SJC: You can do TS algorithmically, but there are complications in spatial analysis that make it hard to provide a ready-made, pre-written function. Reckoning with that has been part of this process, making sure that our recommendations are also user friendly.

JCH: The matrix for temporal dependence is intuitive, reflecting that the past affects the present. In time, we know a priori that ‘what happened before’ shapes ‘what happened today’.

RJF: Exactly!Space is more complicated than time in three big ways. Time has a pre-given periodization – seconds, minutes, hours, days, years, etc – but we don’t know what the spatial units are until you define them. We know how to measure distance between time periods, but doing so in space requires knowing the relevant spatial dimension and how to calibrate it. Time also only goes in one direction – space goes in all directions. The first two issues are huge hurdles for a ‘point and click’ code for spatial analysis.  For TS, some version of ‘T-1, ‘T-2′ in the syntax allows you to call for a time lag because we know all the other stuff.  In space, I can’t even measure correlation until you tell me the units and the relations between them.

APSR: How was your experience of submitting to the APSR?

RJF: Ideal – more than ideal, from submission through publication. The encouraging feedback and careful, thoughtful input made this my best editorial experience with an article in 27 years. Your mileage may vary, of course, but the APSR is (quite rightly) motivated to facilitate the outreach aims of methodology.

SJC: We got specific, constructive guidance on making the paper more accessible — both from the reviewers and the editor shaping the reviewers’ comments. That’s helpful, because the three of us can only get so far without hearing from others.

APSR: Any advice for methodologists looking to bring their work to a broader audience?

RJF: As methodologists, we need to connect with applied scholars and explain the substantive meaning of our methodological demonstrations and advice. After all, what are we doing if we’re not helping other researchers do cool things? Why might an alternative strategy work better? If I’m a sophisticated applied scholar, how will your work help me? Connect each methodological point to a substantive interpretation.  A running example helps make these connections and writing your methods paper like a research project helps people engage.

SJC: The more eyeballs you get on your work, the better. People with all types of understandings of your topic will be reading it, and you want to reach as many of them as possible.

JCH: Going outside your substantive comfort zone is important, too. It pushes you to consider the limits and potential of your methodological ideas.

RJF: Start with part one: ‘Here’s why everyone should pay attention, no matter what you study.’

APSR: Anything else readers should know?

SJC: Don’t give up! If something’s still interesting after six or seven years, it’s worth doing. This was a long process.

RJF: Methods papers can appear daunting to some readers. But we want you to know: you can do this! We’re trying to help you implement your substantive-theoretical contributions.

– Scott J. Cook, Texas A&M University

– Jude C. Hays, University of Pittsburgh

– Robert J. Franzese, Jr., University of Michigan

You can find code for the tscsdep package here.