S7E20 Modeling Co-Development Over Time

[Music] Welcome. My name is Patrick Curran, and along with my as-permanent as a sharpie friend Greg Hancock, we make up "quonitude." We are a podcast dedicated to all things quantitative, ranging from the relevant to the completely irrelevant. In this week's episode, Greg and I follow up our previous discussion of time varying covariates with a conversation about methods for modeling the simultaneous development into or more constructs over time. Along the way, we also discuss back tattoos, right-length closures, 49.5 pound luggage, clear the united lounge, sharpies, neo, the earth-thin-dinger-dinger-donger, living with mommy or daddy, hairballs of science, selfish bastards, licham-senior, phantom variable road trip, the trouble with tribbles, achieving our ideal rank, anthropologies to the Dutch. We hope you enjoy this week's episode. Now for a guy who has all but tattooed on his lower back, early is on time and on time is late. What does late count as? Late is left behind, dammit, and I'm sorry. I'm sorry that I'm running a little bit late. I'll tell you why I'm running late. I had to drop Gus off at Doggie Daycare this morning, and on the way back there was a right lane that was closed. What do I do as soon as I see the sign of the right lane is closed? I get over into the left hand lane because that's what you're supposed to do. But no, all the other ass-****s get in the right hand lane, go as far as they can up front, and then they cut in and they get in way ahead of me. It is not fair and that's why I'm late. Do you feel better now? A little bit. You know what I like is that you became uncorked over the lane, but you took no exception to the back tattoo. I'd have to get the other one removed first. But this is actually a perfect start because we left off the last episode with we were going to open with things that were unfair. Oh yeah. And that was not even planned. It's so organic. But we left off with this things that are unfair. What I love is why everything is a little bit rushed today is as soon as we're done here. You're flying out to LA in what like an hour? We should probably get to work because you've got to get to BWI. I do. And you know what? I weighed my suitcase and it's 49 and a half pounds because I have to be under 50 pounds. And you know what's going to happen? I'm going to go to the airport. Somebody's going to throw their suitcase up there at 54 or 55 pounds and they're just going to shrug and go, yeah, okay, whatever. That is not fair. What are you bringing? Like I pack in a zip lock. What are you bringing to LA that weighs 49 and a half pounds? I just never know which shoes go best with the outfit. But the airport literally represents all of inequity that we face in society. All right, so everybody, picture driving into the airport. What's the first thing you see? Premier parkingness to the right economy parking is to the left. So you go into economy parking. You need to check your 49.5 pound bag that's full of human heads or whatever it is you travel with. There's an opening for gold members and then there are 800 people in the regular line. So you check your bag, then you go up the escalator and you go through security and there's pre and there is regular. Now pre is good except clear is right next to it that have 18 people working there and nobody going through clear. It's a cult. So you get through that. You want to get a Starbucks. You get in line with 20 people and person after person walks by you to pick it up because they ordered on their phone when they were in the Premier parking lot. So then you get out and all the seats are taken in the terminal. But you see people going into the United Airlines lounge right? The smoky glass doors that open and close. What goes on in there? It drives me nuts because my brother travels for work and he gets to go in there and I don't. Then they queue up to get on board and you're in group one. All right, you're still the last person to get on board because they've got the gold and they've got the platinum and they've got families and everybody goes on. You know what my one life line was in this sea of inequity. I always fly Southwest and the thing that I genuinely loved was when you turn the corner onto the 737. Any see any person. It doesn't matter how much you make. It doesn't matter how many human heads you're traveling with in your 49 pound bag. Any seat is open and they even took that away from me. In the new year there will be no more open boarding on Southwest and flyers can pay for upgrades. This is an unexpected amount of therapy this morning. I feel better too. I'm saying this episode may be useless to people but I think you and I have kind of that's been Arctic. I didn't get enough out but it's okay. It's okay. It's okay. It's true. I'm still teed up for some other stuff. But yeah, we did end last time with it's not fair. It's not fair. And we had gone through the idea of having time varying covariates where we have some growth process that's occurring over time and rather than having a time invariant covariate which is just that variable that launches the trajectory off on its own. We talked about time varying covariates which are those variables that might provide the pokes and prods along the way at the different time points. But where it's not fair came in is that we were really just relegating those time varying covariates to be in service of this other variable and whatever process it had. But time varying covariates can have some interesting things going on themselves. That's exactly right. The unfair thing was let's just call our primary outcome variable Y whatever that might be. Let's say it's alcohol use and let's call our time varying covariate Z whatever that might be and maybe we call that anxiety. We build this beautiful growth model for Y in whatever form that might be. Maybe it's linear or curve linear or piecewise or a free bloating. We can do a whole lot of things with that. But the poor Z's they're just given a mean of variance and a covariance and sent to stand in the corner. But what if there is growth in the Z's that we are not representing in the model? That's inequity number one. It isn't fair. The second inequity with the TVC's is Z gets to predict why. So you can say how does your earlier anxiety relate to your later alcohol use. But why doesn't predict Z. There is no reciprocal effect. What if they actually have a predictive relation back to the TVC and the response that any parent has had is life's not fair. Is it? There were two things that you alluded to in the last episode that I want to just lead off with right here. One is historically when someone has said, "Oh, I'm studying change in whatever. I'm studying change in Y." We all kind of just nodded and go, "Oh yeah, okay." But more and more, I think we need to ask people what exactly do you mean by change in Y, right? We can't just give people a pass on that because there's often this gap between what people think they're studying and what they're actually modeling. And that ties to the second thing that you've said. And of all the things that you have ever said, this is one of my favorites. Wait, what was it? It's the notion of the whiteboard. I love the whiteboard. Can you reintroduce the idea of the whiteboard? Not really because it kind of is just what you said. It's a whiteboard. Oh my god, this is going to be so good. Go ahead Patrick. You and I managed to actually write an entire paper around the whiteboard. Yeah. All it is is stand in front of a whiteboard and take a permanent sharpie. So did you hear Trump's thing where he went on a five-minute conversation and a cabinet meeting about sharpies and how they're the best pens and how sharpie reached out to him to make a special presidential pen? So this pen is very inexpensive, but it writes well. I like it. I don't want to give too much publicity, but they do trip me well, sharpie. And later Sharpie company said they've never spoken to Trump. They've never had these conversations and they have no idea what he's talking about. The company that makes sharpies told the Washington Post the conversation the president said he had it at the head of Sharpie never happened. So we're going to take a special quantitative sharpie pen that the Sharpie company made especially for us. And go up to the board and put rectangles in that represent whatever your measured variables are. This is what we have in our data file. This is what is in that rectangular data matrix. If you have five measures of depression, you put a rectangle for each one. Dep one, dep two, dep three, through five. You got five of anxiety. Sharpie them in. If you've got time in variant covariance, a treatment condition, whatever your measured variables are, permanently put them up on the board in these rectangles. Then toss the sharp on the table and pick up a dry erase marker because what we're going to want to do is put some things in and take some things out. There are maybe a dozen different models that go by half a dozen different names that are nothing more than how you take that dry erase marker and connect your measured variables. They are nothing more than alternative ways that you put in double headed arrows, single headed arrows, circles. And when you start thinking about it in that way, it's almost like Neo in seeing the matrix at the end of the first movie. Oh, this model seems really different from this model seems really different from this model, but all we're doing is making a different statement about the underlying process that we believe gave rise to our observed data. I think this is such a powerful idea, not even just in the context of longitudinal models I were talking about right now, but I mean just models in general. What you have done is sharpied in the stuff that we can see, the evidence, the observations that we have, and everything else is coming out of our mind, right? Every arrow that we draw is us saying, I think this is what's going on. Every circle that we might put in, I think this is a construct that's operating in the background. We could have 10 people go up to that board, pick up the dry erase marker, and put 10 different sets of connections representing 10 different theories. We don't know. We don't see the process. The only thing we see are the boxes. So I love this idea just as a metaphor for their things that we see and their things that we don't see. And in this longitudinal world that we're talking about, there are still so many different ways that people can connect these variables. We can even go back to the traditional order regressive cross-slag to model, and that's just one way of connecting the boxes. Picture those five rectangles on alcohol use and five rectangles on anxiety. Now just picture, we're going to have Alcone and draw single headed arrow to point to Alc2. Alc2 to Alc3, 3 to 4, 4 to 5. And then we have the lags, anxiety 1 predicts Alc2 and Alc1 predicts anxiety 2. Put those in with your dry erase marker, that is the order regressive cross-slag model. There are all sorts of limitations to that in a lot of settings, not all settings, but a lot of settings. Your eye twitches a little bit and you say, "I don't like connecting them that way. I got an idea. I'm going to erase those, now notice the rectangle stay there because they're sharpie knit." That's right. "With the special custom quantitative Sherpy pen that we got directly from the president of Sherpy Company." "There are much better pens." Those stay, but now you throw in a couple of circles and point to alcohol use and then you take anxiety and point directly to the alcohol use items, that's the TVC model that we talked about last week. You have a growth process for alcohol use and you're looking at the time specific influences of anxiety. It's exactly the same data and measures. You're just making a different statement. And now what we're saying at the start of this continued conversation is, "What if we don't want that structure?" A good parent shrugs and says, "Well, what are you going to do about it?" And you could look at it and say, "Well, I could erase the TVC effects and I could draw a couple of circles for that represent a growth process for anxiety as well." So alcohol use gets a couple of circles. You're shrugging, you draw a couple of circles under what was the TVC, but is now a second outcome. Nothing has changed with the rectangles. But now you have a multivariate latent curve model. So if we're just talking linear for simplicity, I have maybe an intercept and slope factor for alcohol use and intercept and slope factor for anxiety and those factors co-vari. And that's interesting. First of all, it's not making alcohol use or anxiety more important than the other. It's allowing them to co-develop and the relations across those constructs are kind of interesting. Now again, I'm so enamored of this point that I'm going to keep saying it and then Patrick will edit it out. We still only have the rectangles on the board. Everything else that we've drawn is just our belief about what might be operating. One of the lovely things about the modeling that we do, though, is that the different models that we have imply different ways that our variables should be behaving. The auto-regressive cross-lag panel model implies a certain pattern of variances, co-variances, and maybe means among the variables. The model that we just had, the multivariate growth model where we have growth in alcohol use and growth in anxiety, allowing those to co-vari. That model implies a particular pattern of variances, co-variances, and means. We don't have different data for those two things, but the implications of those models are different. We've established early on that I actually don't know a lot about statistics and I just use analogies for everything. What Greg is talking about is a sausage maker and what is that? It's a thing called a matrix-valued function. The classic one in factor analysis is lambda psi lambda prime plus theta epsilon. That represents a factor analysis. That actually comes directly into play in the growth models that we're talking about now because the growth model itself actually is a factor model. If we have this multivariate latent curve model, literally the model implied co-variance matrix. We have the covariance matrix we observed and we have the covariance matrix that the model believes to exist. Well that is in lambda psi lambda prime plus theta epsilon. What we do is we have this lovely little thing. It's a vector in its lowercase theta and what it is is the IKEA storage system. It's the earth-to-durched ding-dor-dong-dor. Hi, this is Tuberdarsen, linguistics faculty at Northern Arizona University and at the Connotude Swedish Language Consultant. That's definitely not what that means. And it's a vector and it has as many cubby holes in it as there are parameters for the covariance structure. And you run that vector through the saucy breaker, which is lambda psi lambda prime plus theta, and it pops out the model implied covariance matrix. So the autoregressive cross-lag has one sausage maker, the same rectangles but a different earth-to-durched ding-dor-dong-dor. Nope, that's not even the same wrong thing you said before. And then you have the TVC and you have the multivariate and each of these gives a different model implied covariance matrix. Now it's a little tricky because some of those are nested where you could do a likelihood ratio test but quite honestly not many of them are because you're changing too many knobs at once. Okay, okay, okay, okay, okay, okay, how do you get William Niesim to say that? A Kai-K. But I would say as far as co-development goes, allowing each of those factors to have their own growth process maybe is a little bit more fair, but it still might not correspond to our actual question about what's going on or our theory about what's going on from the perspective of change. Oh, dude, you're spot on because every time you erase part of that diagram and draw in a new one, you're not just changing the sausage maker and what the implied covariance and mean structure is you are making a fundamentally different statement about the hypothesized theoretical model of change. So when people start saying, oh, estimate all these models and pick the one that best represents the data, absolutely not because you're making fundamentally different statements about the underlying causal process that you believe gave rise to your observed data. So in the multivariate latent growth curve model, we would have to have some belief that there is a growth process operating in both of those and those growth processes are related and the relations that we're talking about are really at a between level that I have a certain amount of growth in my alcohol use, I have a certain amount of growth in my anxiety. You have a certain amount of growth or change in each of those, everybody has a certain amount of growth or change in each of those things. And then when we see a positive association, let's say, between the growth on those things, what we really mean is that people who tend to be higher relative to others on their growth on anxiety are also the people who tend to be higher on their growth or change in the alcohol use relative to other people. So this is a model of change and that change is something that's occurring within individuals, but the relations that we're talking about are really at that between level and we have to have research questions that are targeted to those levels. And this brings us to our next advanced topic in mathematical statistics, which is do you want to live with mommy or do you want to live with daddy? Too soon. Too soon. And what I mean is Greg beautifully described this notion that the individual variability in these trajectories and how they relate to one another is fundamentally a between person characteristic. But be sure to subscribe to our channel. Beyond that, it also is not linked to time. So we talked about that in the prior episode, is John Stuart Mill is spinning in his grave because I have an intercept in a slope and you have an intercept in a slope, but they are not subti, right? They are not linked in time. So now picture two versions that we've drawn on the whiteboard. We have the time varying covariant model where we have a growth process for Y and we use Z as a time linked predictor of Y. So we can have Z at time one predicting Y at time two and so on and we talked a lot about this in the prior episode. But the kids said that's not fair. I want a growth process for anxiety. - No fair. - And so we say, okay, we're gonna erase that and we're gonna build you this growth model for anxiety. Are you happy? Now there's individual variability in growth. Now call users individual variability in growth and anxiety. There are you happy and the kid says, but where did time go? I don't have a link to subti, there's no temporal precedence. It's all back to these between-person characteristics. So we are forced to choose and it really is a forced choice. Do you wanna build a time lagging with the TVC or do you wanna lose that and build a growth process for the TVC but at least in traditional settings, you can't have both. - At least in traditional settings, he says. So are there models then that can serve as hybrids between the growth structure that we're talking about and some of the causal elements? Are there ways to try and pull that T back in? - Yes, there are. (laughing) And we have been trying to figure this out and I mean we writ large. My fingerprints are on some of this, but a lot of really good people have done a lot of really good work in this and I've hacked up a couple of hairballs that have tried to address this, but it was just in a giant pile of hairballs. The hairballs of science, I now see a new book. Someone out there can write it. - That's your best script. (laughing) (upbeat music) (coughing) - Science. (upbeat music) (laughing) Here's the thing and this is kind of where I started thinking about all of this as a whiteboard problem. This goes back years and years ago, but quite honestly, I was a selfish bastard because I was working with real data on a real question. We were looking at some of the stuff we're talking about depression, anxiety, and delinquency and adolescence. I fit an auto regress of cross-life model, old school. I fit a TVC growth model and I fit a multivariate growth model. I had all three of these as different options for representing the data and none of them were completely satisfactory to me. I literally, now this isn't even figuratively, I literally was working at a whiteboard and I thought, well, what happens if we took these growth processes in a multivariate LCM and we leave them as they are, but we just chalk in by directional relations at the level of the variables of the time repeated assessments. So we have a multivariate growth model. Alcohol use gets a growth process, anxiety gets a growth process, but I just walked up and drew in alcohol and predicts anxiety too. Anxiety one predicts out too and I marched it down the set of measured variables. I just drew it in and I thought, huh, I wonder if that's identified. And so I kind of dinked around with it a little bit and it was like, that's a lot of arrows. Well, that's a lot of arrows. Although most of them are fixed, right? That's true. Because they're the factor loadings, they're not estimated. These models look much more complicated than they actually are because of how many things were fixing and restricting in them. So I dinked around a little bit and I kind of convinced myself that it was identified and then whenever I start getting confused, I try to sub-con the workout to somebody who's smarter than I am. And I went next door and sat in Ken Bullin's office and I sketched some of these things out and that became the auto regressive latent trajectory model or the old model. In theory, it's the best of both worlds. You've got the growth model, you've got the variables hooked up to each other in an auto regressive way, everything you could possibly want all in one place. The model is absolutely an unambiguously correct and you can't see me using air quality or a big gun. Well, actually not because he's watching cap videos whenever I'm talking. (screams) But it is correct because all it does is put a few more elements in the Inker-Dinker, Frinkstink, Dorker, IKEA storage system. Test, no. And it runs it through Sigma Theta and Mu of Theta and it gives us a new covariance matrix and a main factor. And so from that sense, it's just an alternative representation on the whiteboard. But we wrote some papers on this, Ken did some really nice work on it as well that I was not involved with. He was working with some other colleagues and so there are lots of ways that we can work with this model. But I started to not feel completely comfortable with how it related to the underlying theory of change over time. And I've written about this and I'll put up a few papers in the show notes that describe it. So I won't go into the bloody details here. But anybody who's up on their path tracing rules, it should make you squint a little bit when you think about what I described because I was super clear in saying that I put these regression parameters in at the level of the measured variable. What that's gonna allow is the mean structure and the covariance structure of one construct to leak across to the other construct. That is, it's exactly like the time varying covariant model in that now that growth process of anxiety is in part being impacted by those lag defects from depression and the lag defects from anxiety to depression are affecting the growth process that underlies alcohol use. All right, and so what that means is picture the growth in depression, anxiety without those autoregressive effects. You get a mean, you get a variance, you get a covariance. When you put those autoregressive effects in, those means and variances and covariance has actually changed. And indeed, it can even change the shape of the trajectory. There was somebody a number of years ago who went after us about this thing and wrote a fairly critical paper is very well done. But it was pointing out that you could have a curvilinear trajectory in one of the constructs and the autoregressive among the observed repeated measures would account for that and it would look linear when it was actually curvilinear. Can I wear aware of this, right? I mean, that's part of the model when you do the matrix algebra sitting right there. But I started to feel uncomfortable with that because those autoregressions were actually changing how we were thinking about the growth process itself and I wanted to separate those. And we do this in the multi-level model of the time. We talked a little bit about this in the last episode. The within-person process is orthogonal to the between. And what that means is as we build the within process, it doesn't change the characteristics of the underlying growth. You have the trajectories of depression, you have trajectories of anxiety and you kind of dink around with all those effects if they're orthogonal and it won't change those underlying trajectories. I went back to the whiteboard and I had a memory of a wonderful guy named David Rinskov. I think you know David. I do. David is a remarkable guy. Great guy. He's made wonderful contributions to many, many areas. But to my knowledge, he was the first one to propose the phantom variable. (laughing) Just the coolest name for anything in our field, right? Besides being a Star Wars title, I think, it wasn't that one of the 18, the phantom variable. Is that number one? I'm trying to remember which. Number one that came out eight, I don't know. (laughing) At last we will have revenge. He came up with this incredibly clever way of creating what were functionally one item latent factors. There aren't latent factors in the way we usually think about them. And I thought, well, wait a minute. What if I used phantom variables for the time-specific residuals? You have been well-trained, my younger apprentice. So we're gonna move into the residual matrix that is representing those within person effects. What if I make those latent variables, I could then use one residual to predict another residual. So instead of the variable predicting the variable, I'm gonna jump it up into the residuals and being the incredibly artistic creative clever guy that I am, I called that the latent curve model with structured residuals. Wow. My pet growing up was named Cat. (laughing) I have to say, this is probably my favorite of your hairballs of science. (laughing) I mean, it really is. This is such a clever idea because in the alt model, as you said, the variables are connected. And we know from some of the discussion around the autoregressive cross-lag panel model. We know that that has a difficult time sometimes separating out what are the between processes from what are the within processes and so what you did is to move everything into the residuals where you brought it to the individual level. It is my level of aggression at time to above or below my own trajectory. So it's relative to me, not relative to anybody else. And so yes, yes, yes, blah, blah, blah, orthogonalization, yada, yada. What you did is a very clean separation of within and between. So if someone thinks that their own alcohol consumption is a little bit high relative to their growth trajectory or a little bit low relative to their growth trajectory, it's that thing that you are relating to their anxiety, whether it's high or low relative to their own growth trajectory. So you succeeded in making this a within aspect of the model and it's one of my favorite hairballs for sure. Well, I appreciate it. And when I say I, that's just an abject lie. Is this was it takes a village kind of thing. A lot of it came out of my work with Bowlin who really helped me with the analytics. If you've seen our old paper, it's Bowlin and Curran can took the lead on that. And it's actually very technical in the developments and that was all can helping me understand that. And so a lot of this came through Ken's help, but also a ton of collaborators. Andrea Howard worked very closely with me on this. And she had pretty darn near equal contributions that couldn't have existed without Andrea's help. And then Sierra Bander, Stephanie Lane, Jim McGinley, that was very much a group effort. But the thing I really like is jumping up into the residuals, those order regressions and those lags, they don't impact the growth factors anymore. The means don't change. The variances change a little bit because it's related to the covariance, but it's just maximum likelihood trying to balance weight on the ship. You know, as I mean, they'll change a little bit, but I'm not kidding with the old model. Like you would do the unconditional growth and you would write a discussion section about what depression was doing. But in the old model, if you bring in those in the way I described, you can have a completely different implied growth function and depression when you bring in anxiety. It's correct. It's up to you as to whether that's what you want or not. Right. Because there's situations where you would. Routin Bush has an amazing example with TVCs where he wants to model trajectories of reading ability and children, but he wants to account for the time-specific effects of how many days of instruction a kid missed. Because in lower income families, it's much more likely that you're going to miss school. So he wanted to look at growth in reading, having adjusted for that time varying covariate. He wants the means and the variances to change. That was the point. So if that's what you want, the old model is spot on. And again, Ken has gone on to do some really lovely work of using this as a general framework to get to a whole bunch of different models. All I'm saying is for the kind of questions I tend to think about, I don't want those to change. I want to treat them as separate. There's a within person process and there's a between person process and through the parameterization of the model, meaning what we draw on the whiteboard, we can orthogonalize those so that they operate separately. One of the early points that we were trying to make in this episode is that how you wind up connecting these variables is tied to whatever your belief or whatever your question is. So if I said multivariate growth model, what would the shape of a research question be for someone who wanted to run something like that? What I would say is you are interested in how two constructs travel together through time at the level of the individual. If you are accelerating in your reading ability, do you also accelerating your math ability? Do those two things travel together through time, but you are fundamentally not interested in does earlier reading ability predict later math or does earlier math predict later reading? You are just saying I'm going to let reading do its thing. I'm going to let math do its thing and see that if kids who are increasing more steeply in one, do they tend to increase more steeply in the other? I like that answer. So then we move to a hybrid model like the alt model. You are telling us a little bit about a question. Can you say again that if someone were choosing the alt model, what would be the shape of the question that they would be asking? I mean that one's tougher, which is why I started trying to expand it. It's more of an aggregation of between and within. I came to see that as a simultaneous expression of the data, where does your earlier reading in part predict your later math in the presence of everything else that's going on? Using MLM like language, it's an aggregate effect. You're not cleanly separating the within and the between person. One of the things you said earlier about path tracing is so beautifully evident in all of these models. If I was asking in a multivariate growth model, how is time to alcohol use related to, you know, whether it's time to anxiety or time to be anxiety? I'm tracing up through the growth process and how the growth processes are related and that's where those things are connected. When I get to the alt model and I do my path tracing and I say something like, how is time to alcohol use related to time to or time to be anxiety? I might be tracing in part through the growth process. I might be tracing in part through the auto regressive process. So there's things that you have to believe are operating simultaneously. And now I move to the liquor sir. Which is what Greg calls the LCMSR. If someone's calling something Rickle Pym, then we're calling this liquor sir. But I got to tell you I think it was a missed opportunity because I am on day 522 of duo lingo and I'm trying to get my Spanish back. Wow. Really it should be lychem senior if it's the SR. I mean, if you're going to be accurate about it. Actually, I am calling for it right here and right now. It is Rickle Pym and lychem senior for our international audience. Great. So when we move to the go ahead, lychem senior. Tell me the shape of that research question for the model. Well, my theory best corresponds to the lychem senior model, which is I believe there to be an underlying continuous developmental process that in part determines alcohol use. And in part determines anxiety. There's individual variability and starting point and rate of change in each and we want to relate those to one another. That's the standard latent curve part of the model. But I also am exceedingly interested in if you're higher in anxiety than you usually are at time one. Do you tend to drink more alcohol use than you usually do at time two and what we're doing is picture each person's trajectory with their observed measures humming around it. We're saying that if your dot your observed measure on anxiety at time one is above your trajectory. Is that associated with your observed value dot being above your alcohol use trajectory at the following time point. So if you're higher than you usually are on anxiety, do you drink more than you usually do on alcohol. And then we're averaged in that over people and we're running both ways. If you're higher on alcohol use do you tend to experience more anxiety and those are the reciprocal effects. And for me, it's very near. It's not all the way, but it's very near to a lot of questions that we really do ask at a theoretical level whether we even know it or not. Is we're not interested in between we're not interested in within we're interested in both and how those jointly reproduce the characteristics of the data that we observed in our sample. Okay, wait, wait, wait, you said you're not all the way there and your wife says that you don't listen when other people talk. I am so proud of you. Yeah, because here's what it is. It's not a limitation of the model. If what I described is what the question is that you're after. But here's that weird little thing. And I have to fight myself from saying this. We have to be very careful about how we interpret the lichens in your effects. I was very clear that it is if you are higher than you usually are at one time point on one construct are you higher than you usually are on another construct. And I always say higher, these are symmetric. You could be higher and lower, lower and higher, right? What we cannot say and I got to tell you we really want to sometimes is that if my anxiety increases between time one and time two, does my alcohol use increase between time two and time three? That is a fundamentally different question that lichens in your has no ability to avoid. evaluate. Yeah, and what you're trying to do is to start to bring T back into the change process. Right? Because as it stands right now, if we have this growth trajectory that cuts across all of time, there isn't a subti. When you start talking about the change from time one to two and two to three and three to four, we sort of are getting our subti's back, but it's now in terms of change. It's not where we are in terms of a level of a particular variable, or where we are in terms of a level relative to our own trajectory. Now we're literally breaking the trajectory up into the pieces that happen across each of the time points. And in order to do that, we need to, well, we need to go up to the whiteboard and erase all the stuff that we have on there and now start drawing a different model. And enter from stage left the latent change score model, which came out of the remarkable depths of Jack McCartle's brain. There were a number of other colleagues. Again, none of us work in a vacuum as sure there's Millio Ferrer and Kevin Grimm and Hama Gami. And so there are a lot of people involved, but it really was Jack was the lead of that. And what I love about it is what is a line? This is so fun because Greg and I are like almost at the peak of our careers. Like we can't go any higher. Mostly because of incompetence, we use eighth grade math in most of what we do. What is a line? Well, it's rise over run that is equal between each time point. So change between one and two is equal to change between two and three is equal to change between three and four. That is a line. Right. So we can have a linear trajectory where we compute the time adjacent change and set them to be equal. Yeah. And what Jack said was, well, wait a minute, that's still a whiteboard problem. We're still working with the same rectangles. He's going to draw and I got to tell you it's like him and Rinskov renting a van and a keg a beer and like taking a road trip across the country with Phantom variables. If you look at a path model for one of these things, I mean, it is like Phantom variables gone nuts. Oh, yeah. Completely. I'll refer to something that you would relate to. It's a trouble with tribbles. Oh, it is. The trouble of tribbles is a classic episode from the original Star Trek series in the 1960s. There must be thousands of them. One million, seven hundred seventy, one thousand, five hundred sixty one. So the tribbles all they did is they reproduce like at a very high rate. And so Phantom variables are reproducing at a very high rate. But what the latent change score model does is instead of saying is your relative standing at one time point predicting of your relative standing at another time point, which is a very important and valid question to ask is just saying does your change between two time points on one construct relate to your change in the following time points on the other construct. It's a different path diagram, but it's a different theoretical question. It's a beautiful model, one that we could spend a lot more time talking about, but I love it because it gives us flexibility to look at co-development that we don't otherwise have and more local co-development, right? Because the influence that change in one variable has on change in another might be different earlier in the process that it is later in the process. And we can't get that when we're operating at the level of a multivariate growth model. So I love that we're getting all the way down to that. And also it is possible, as Patrick alluded to, to constrain this more flexible latent change score model to get some of the more traditional growth models. So that's a point worth making. The other point is you said we're at the peak of our career, oh honey, you peaked so long ago. I didn't say I didn't. I mean, it's awesome toad is not bounded. It's infinite, right? Okay. So that I just to be clear, there's some phrase in the military, I don't remember what it is, but there's some phrase about when it's written in somebody's record that they have achieved their ideal rank. Means that they shall go no farther. I think you and I have achieved our ideal rank. Maverick, 30 plus years of service, you can't get a promotion, you won't retire, and despite your best efforts, you refuse to die. You should be at least a two-star admiral by now. Yet here you are. Captain, what is that? It's one of life's mysteries, sir. Now I got two thoughts. One is some of you may be saying, well, wait a minute, right? And when I say some of you, I mean like the country of the Netherlands, are saying, why are you not talking about Rickl Pym? If you're talking about Lycombs, senior, why are you not talking about Rickl Pym? Well, Rickl Pym is a wonderful, lovely model. We interviewed Ellen Hummacher what a year or two ago about dynamic SEM and she does amazing work and she has that incredible paper. I think it was in 2017 and psych methods on the autoregressive cross lag and then the random intercept autoregressive cross lag. It shares a lot of similarities with the LCMSR. These were developed independently. She was working with her group. I was working with my group. But why we haven't talked about it in a lot of detail is there is actually a pretty big difference between the two that are not evident in the path diagrams. A lot of people say, oh, they're the same model. It doesn't matter. They're actually not because in the LCMSR model, we continue to restrict the mean structure in a very strong way. We literally remove the means from the repeated measures and we force the model to reproduce them solely through the mean of the latent factors. That is the cardinal characteristic of what makes a latent curve model, a latent curve model. We are reproducing the variance covariance structure but we are also reproducing the mean structure. Because Rickl Pym grew out of the autoregressive cross lag tradition, the mean structure there is actually saturated. So no restrictions are imposed on the means and you're focused on the variance covariance structure but not the mean structure. That's neither good nor bad. It's another statement. It's another way of drawing on the whiteboard. But that might be an interesting future episode of the broader question of what are the means bringing to the party. Why are the means so important to the Likim's senior model but are saturated in the Rickl Pym model? Lots more to talk about. Are apologies to the Dutch but we will come back and talk about that on a link. And the Swedish and the. I'm sorry we don't have enough time to do an alphabetized list of apologies. Sharpie and yeah. But the other thought is you seriously have a plane to casual. This is not a figurative gag. You actually have to take my 49 and a half pound bag. All right thanks very much everybody. Hey thanks everybody take care. Bye bye. I think you actually mean "Haggorts befolk niks te treetningen." Thanks so much for joining us. Quantitude is brought to you by additional office products that um pardon me excuse me sir I was holding the mic excuse me mr. president please. I talk to the quantitude guys Pat and Craig great guys they said sir would you reach out to your friends at Sharpie and have them make us a pen. I said sure if you have jiffy on the show more I was talking to jiffy a week or two ago he called me in the oval office he's clearly the real intellect behind the podcast success he'd make a great running mate actually. He suggested a full range of office supplies which isn't a bad idea. I was envisioning a quantitative stapler. I actually dated the sister of the founder of swing line which is the Cadillac of staplers in my opinion. We'd have to look into getting gold staples of course or how about quantitude paper clips like in the shape of a curly cue for quantitative. I love paper clips. I used to use them as money clips when I was a little kid until I got my first money clip from my grandfather for my fifth birthday. I'll never forget when he said to me DJ he always called me DJ because he was a big fan of Dwayne Johnson and Derek Jeter DJ he said always listen to great podcasts your grandmother and I especially love those guys on the quantity so I've been a huge fan since probably the early 60s what about a quantity three hole punch or quantity sticky notes. I can talk to the president of post it and see if he can make you guys something extra sticky. 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