Regression to the Mean Girls：混合効果モデルとLove Islandのキススコア（ゲスト：Hannah Barton）

This is Regression to the Mean Girls, where we chat with brilliant data people about their silliest side quest. We're mean as an average, but actually very nice. Come sit with us. I'm Lucy D'Agostino-McGowan. And I'm Sarah Lotzbeach. And today we're really excited to be chatting with Hannah Barton, who is a PhD student at the University of Washington. And I believe, so I saw that your background is in speech-language pathology, right? Yeah. So what is your PhD in? The theme or something related? So the program is speech and hearing sciences. I mostly work on language development and neurodevelopmental disabilities. So specifically right now, I'm very much in the autism world, but I've also worked on like Fragile X syndrome, fetal alcohol spectrum, things like that. That's incredible. Well, thank you so much for being here today with us, Hannah. Yeah, thanks for having me.

So to kick off, we usually break the ice with what we call a media minute, but tends to skew more towards a media many minutes if we really get going. So we prompt this as, what kind of media are you enjoying right now? Books, TV, movies? Hi, since this is our first recording of the fall, I'm going to talk about, there's a new season of Ted Lasso. I don't know if anybody watches Ted Lasso, but I really thought we'd close the door on that a couple of years ago, and now we're getting a new season. Now it's a women's team. And I am enjoying the new Ted Lasso. It's one of the only things I watch probably that is actually current and comes out weekly. And I have to have some sort of control. Yeah. We are also watching Ted Lasso in my household. And I also thought it was going to be done years ago. But we're hanging on. So we'll see how it carries on. If you're a fan, I recommend if you're ever in London, there's a Ted Lasso tour of Richmond. There's, like, one lady because, yeah, apparently for whatever reason, Ted Lasso never really caught on in the U.K. like it did in the U.S.

And so there's this one lady. She is the official Ted Lasso tour of Richmond. And she takes you to all the filming locations. And also Richmond's just, like, very ritzy, very nice. We toured the – or we had a drink at the pub that floods, if you've ever seen that. Like, on social media, there's, like, a pub right on the River Thames that when the tides come up, it floods. So I highly endorse the official Ted Lassiter Tour of Richmond. I can go next and keep it on the women's sports theme. I've been watching the WNBA playoffs, which are good fun. And as a Seattle Storm fan, I am not invested in it at all now because we aren't very good this year. So I'm just having a fun time watching everyone and hoping everyone has fun. That's awesome. I think you're the first person to use sports as a media minute. It was kind of surprising. Maybe it was our timing before because we recorded over the summer. Maybe there were fewer sports opportunities in the summer. But that sounds awesome. No, because we did like March, which had like March Madness. Like some people. Even I know about that.

So I think it's just our, I think it's selection bias, but good that Hannah's in here. So we have sports media. I am going to. So over the summer, my brother and I read Children of Time together, which is a sci-fi book, which sort of got me back on. And I historically have done a good amount of sci-fi reading. And a lot of like, I really, I went through a phase like two years ago where I read all the Isaac Asimov short stories. And anyway, so this got me like, recently, my brother also suggested that I read some Philip K. Dick, which I had not actually ever read. So I read Do Androids Dream of Electric Sheep, which is like the book that Blade Runner is based on. Although I will say, I loved the book. I had not seen the movie, which is surprising, because it feels like it's one that I would have seen. And I watched it after. And I, like, loved the look of the movie. Like, I liked that vibe. It was, like, steampunky. I don't know. I liked that. But I liked the book. Like, the movie really changes, like, what the meaning is, which was interesting. And then I read The Minority Report, which I had already seen that movie.

But anyways, and then I started A Scanner Darkly, which was too dark for me. So I had to stop. So I'm now looking for new sci-fi adjacent short stories or novels, if anyone has recommendations in our listenership. I mean, not sci-fi related, but I did realize chatting with Hannah before you joined that one of the only books that I read that you might have had even the slightest bit of interest in is like kind of related to today's topic. But it's like, I think, is it technically satire? Have you read it, Hannah? The Compound? Yeah. Yeah. So I think it's satire that blends, like, Animal Farm and present day. So it's certainly not sci-fi because, unfortunately, these are real people, and I suppose, in a way, these things could happen. But as I said it, I was like, that's one of the few books that I've read that Lucy might like. With all her energy to sci-fi. Yeah. Yeah. Yeah. Mm-hmm. I can see why you would think I would like this.

What a Korean novel makes you not like it. Yeah. It does actually say it won Goodreads Choice in science fiction. So I think someone would consider it science fiction, but I don't know. I'm just looking on Wikipedia. Not me, but cool. Yeah. Nice. Great. Well, this was a successful media minute. So our last several episodes, which we kind of recorded in succession a semester ago, I was really stuck in a loop of only consuming the same media. So good thing that we can now do a little more diverse. Well, thank you again for joining us. Do you want to give us some context for your deep dive? Yeah, absolutely. So I'll give my personal context and then I'll say what Love Island is and all of that. Perfect. So this past spring, I was finishing up my dissertation prospectus. And for that, I'm using this model called the social relations model that we're going to talk a whole bunch about because it's what I used for this.

And then I was doing that and I thought, wow, I don't want to think about any real data or any language samples or what kids say for like a little bit. And we were coming up on summer and I thought, oh, my gosh, Love Island's on. Like, what can I do with Love Island? And I thought back to this fun challenge that we're going to talk about today where people kiss each other. And it just occurred that this is like the perfect data set to do this kind of analysis on. So this whole thing was really done on just feeling like I should probably start figuring out how I'm actually going to use this model. And I want to do it in a fun way that is not actually thinking about real data or all of the complications that come with dealing with real people and all of the things that they say. So that's kind of the impetus for what I started doing. And basically, this whole thing centers around the show Love Island, which I think, I don't know, you guys know a little bit about it, but I can explain kind of the whole thing. So it's essentially this reality show. There's versions originally in the UK. There's one in the US.

Doing this, I learned there's one in Malta, but I've never seen it. So that exists, too, which is great. And all of these shows, basically, they have a fancy villa and they dump like 10 to 12 really hot single people. And then they say, you guys couple up. It's like five men and five women. And they couple up. And then about every week or so, they say, now you recouple. Like, find a new person, pick the same person. Maybe the women pick. Maybe the men pick. Maybe the public votes on who's coupling. And usually as part of that, people get voted out of the villa or they get dumped from the villa or various things. And I think the key thing about this show is it airs six days a week. so there's so much content and you really are just like you're in it with them and also no one's watching it that carefully because it's at least six hours of content a week it's too much content so you're just getting so much and throughout each week before the eliminations or anything like that they're doing various challenges so like a lot of times they have ones where they all like crawl

through slime and then sometimes they like baby bird feed each other like ketchup which is just absurd to say I'm sure there's other ones but those are the ones that really stand out over the course of a season and then they do all kinds of like diabolical things where like there's a dumping and they just make the most popular three couples choose a couple to dump and they're just Like, send one of your friends away. So there's all kinds of wacky interpersonal dynamics going on. And the last element is that throughout the show, which goes on, like, all summer. So this is, like, six episodes a week, every week, all summer. They're sending in more people. So they're dumping people from the villa, but then there's new people coming in who are called bombshells. And those are, like, additional hot people that they can then couple up with or flirt with or whatever. So that's kind of the premise of Love Island. on the whole what i specifically looked at is one challenge that's called the kissing challenge

or i think sometimes it's called kissing booths i don't know and they do this on a lot of the seasons there's many many many iterations of this challenge and it's essentially like either all the men or all the women become like the kissies or the people who are going to be kissed and all of those people put on blindfolds and headphones so they can't see anything and they line up and then the other gender goes one at a time, and they just kiss everyone, and then the ones in blindfolds give a score, and they note it down. Oh, this is amazing. And it's a perfect data set. If you're having trouble visualizing this, I do have some pictures of it happening. Please, if you would like some context, let me share. Yes, we'll put these in. We have, like, a little blog that you'll be able to populate, and so we'll get these pictures so that the audience can enjoy. enjoy no it's gonna make it not a thing and I unfortunately don't have a double thing so we're just gonna look at it and yeah that's good google drive so this is like all the men lined up with their blindfolds and their headphones on okay and then this is what it looks like when they're

actually kissing which it's weird to watch as an audience member you're kind of like this is not something I should be watching but you watch it anyway or you do your chores while you're doing it and then they end up with this lovely table that they fill out in the moment of each score that each person has given each other. Do they score, do they do it, like, one at a time, like, right after they say their score, or do they have to, like, remember 5, 4, 3, 2, 1, or whatever, recall bias? I was, yeah, I was re-watching this just to make sure that I knew all of the weird things that happened, And I think the way it works is, like, one man goes down the whole line of women, and then all the women take their headphones off and give their scores for that man. Which does sometimes, like, there's a few instances where the early on women say something in giving their score that the later women.

Yeah. Yeah. So that does happen. Love. And it's super mixed in terms of what happens. So, like, there was one where someone said something and then someone down the line was like, wait, that's not who I thought it was. Like, and then it changed everything about how they were scoring and what they were doing. So it's good and silly. And lots of social dynamics happening. Messy data. Yes. Yeah. And the other messy thing that they do is like sometimes you have people who say like I having interpersonal conflict with this person I not going to kiss them or I going to kiss them really poorly or i going to kiss this person really nicely because i interested in them and then sometimes the show will throw an extra element in so one of the seasons we're going to talk about today instead of just having all the men who were already there kissing all the women they actually took away the last man's turn and they'd brought in a new bombshell man and have him kiss all the women instead.

Yeah. Oh. So there's all kinds of, like, fun, wacky elements to this kind of data set that make it just, like, perfect for this kind of analysis. And I think you could, I mean, you could do so many other kinds of analysis on this. But for me personally, I was looking at dyadic interactions, and this is, like, the king of all dyadic interactions. Yeah. Okay. Can you explain to us what dyadic interactions are in general? Absolutely. Yeah. So basically it's just anything where two people are talking, interacting, even like just looking at pictures of each other and judging them. It's basically just the idea that like when two people or a person and some stuff are interacting with each other, there are multiple things at play. It's not just like me talking into a void, you guys being there also impacts how I talk and then what you say influences my speech and on and on and on nice okay that makes sense I can get back so these are this is like some kind of

pairing due to differences in both maybe the estimates themselves and how correlated they would be expected to be based on the fact that some of them like if you have multiple estimates across the same people that are yeah I think I understand yeah yeah so can I ask so I definitely can see like is it dyadic is that how you said it yes yep so dyadic interactions is that kind of like the top the down the line where like the first person's response might inform the grade that like a later no it's kissing yeah so it's it's specifically the two people kissing are having a dyadic interaction and then because the other is one-sided that it doesn't count because it feels like if like i inform order answer and lucy informs my answer then it would also be a dyadic interaction or no? I think you could frame it that way. I think the problem with that has been, like, I would frame that more as an order effect than a specific, like, dyadic interaction because you just end up with, like, exponential dyadic interactions

if you consider that, like, the first person is then impacting six more people down the line, which impacts the second person and then that impacts four more people that are, like, whatever you want to call it. So, yeah, that part, I... don't have modeled at all, and I have no idea how to go about modeling it because it's just, there's so many different things happening. But there is one aspect of the social relations model that captures some of that messiness, but it's not great. Cool. Thank you. Yeah. All right. Shall we jump into some analysis? Yes, please. It's down a rabbit hole. Great. I should have also said that the scores are out of 10. So that's kind of the basis of how they're being scored okay so the social relations model is both like a theoretical or like a way of approaching these kinds of dyadic interactions or just like social perception in general so as far

as i can tell it's big in the like intergroup psychology and like perception of others world and it's basically the idea that when you have these kinds of dyadic interactions where anyone is talking to someone else, giving each other a score, those kinds of things. You can separate that score and the variance in that score into the actor component, which is like the person giving the score, the partner component, which is the person being given a score about or the person being interacted with, and then a relationship component, which is like the specific special spark that two people might have, and then you have the error component. So it's basically this idea that you can divide up the variance that way, and there's a bunch of different ways that people go about getting those estimates depending on what the design is and all kinds of things. Most people, I think, are using essentially multi-level modeling

and using both, like, the actor and partner as random effects and then adding in other predictors as fixed effects. But it seems pretty variable. And then there's one really good simple package on R called RRR that runs, I think it's like the method of moments estimation. Yeah. And so they use that, which is really nice and easy, but it's very specifically for only perfectly round-robin data, which is where everyone's interacting with everybody. and there's not really any missing data and it's all wonderful and good, which is not a reality most of the time. So that's kind of a broad overview of the social relations model. Okay, can I ask a question? It makes so much sense. It's the first time I've heard of these models. I'm so excited. We learned about so many different ways that we can use, like the same statistical tools for different things.

So in the most common case that you said was setting like a multilevel model. So we're going to have like a random effect for the person, the kissy and a random effect for the kisser. The part that I'm trying to disentangle in my mind right now is you said that we can separate out the kissy effect, the kisser effect. That makes sense to me because we have repeated measures for each kissy and kisser. And then we've got an error term. Also makes sense to me. The part that I'm struggling with is how do you how would you quantify the kissy kisser interaction when like because you only would have one measure per. Right. Or am I wrong about that? Yeah, so the answer is you can't in this kind of case. Okay. So the theoretical construct is that that exists separately. Yeah. In this case where there's only one score, you can't do it. So you just get this big giant chunk of relationship and error. So if you look, this is actually just a breakdown. So this is treating it just as a round robin. So this is the first thing I did. It's just like let's pretend it's perfect, wonderful data.

Let's just look at the components. and that relationship variance is huge it's like 70 percent of the variance but that includes error variance and there's just no way to separate that as far as i know which was a big i looked at this and said man it's a great thing i'm planning to do multiple measures in my dissertation so i can yeah we can disentangle yeah this is so cool though and like i do think also you you couldn't disentangle it, but you could think through magnitude. And, like, this, to me, and I could be thinking about this very naively, but I'm looking at, so we'll put these again in the show notes for our listeners, but we've got a kind of small sliver of actor variants of maybe, like, three or four times that sliver of partner variants. And then I would say, like, 75% of the space is taken up by this relationship variant. And if I'm just, like, intuitively looking at that, I would not expect the error, like, to be, like, I would expect a good chunk of that to actually be relationship variance

due to the magnitude of the actor and partner variance. Because once we've, like, accounted for your individual differences and your partner's individual differences, like, what would there be, what would, like, conceptually, what would this other error be as not the relationship? You know what I mean? So I do think we can make some kind of like at least magnitude type of discussions as a maybe not absolute discussions about the relationship variance size, but we could sort of say that it's probably big. But would that be where the ordering currently falls? Like if we think there's that ordering effect of like your scoring being informed by people who answered before you? I was trying to think of, to your point, like, what would cause me to erroneously report a score if not, yeah. Yeah, so that's where it gets funky because that relationship variance is just like special sparks with those people. And that special spark could be, wow, you kissed really, really well together and that was great.

Or it could be, man, the person before me said that you did something that you didn't do to me. And so now I know that you didn't prioritize me in the kissing challenge until I'm going to give you a lower score. and I think both of those would fall into relationship variants and both of those things happen. So it's kind of a mixed bag. I guess, too, like, Sarah, you're saying that, I mean, I would think, because we only have one, everyone, does everyone stay in the same order for the, for the, okay. So I would think, like, the ordering effect in terms of just, like, you were third, you were fourth, you were fifth, that should be in the actor variants because it's constant. Like, I think, right, it's constant for you. So what if it's specific? But the specific, yes. So the order of, like, you were third, you were fourth, you were just that piece, I think, would be in the after variance. But the, like, someone said that they were nicer to me, and then, like, that influencing, that makes sense that that would be in this relationship, because that would be different. Like, that didn't happen consistently every time.

But if there was, like, if there was just a constant ordering effect that, like, being third makes you, on average, score lower or whatever, I would think that would sort of get subsumed into the actor variants because that actor was always third. And so they went both ways. It's like what if it's out? Yeah. Or what if it's like a almost like a like a regression to the mean, like with self-report? If I ask you, like dietary intake, if you're worried yours is too high, you'll go to the middle. If you're worried yours is too low, you'll go to the middle. Like what if you had a higher score for that person? And then when they give a low score, you're like, oh, maybe I'm like maybe my standards are wrong. and like you lower you know what I mean like if it's not a consistent shift in the same direction I wonder does it cancel out sorry no and I would say though there's a bunch of times where people are giving widely different scores like they're pretty comfortable with like one woman saying like that was terrible that was a two and it's pretty clear that it's because she knows who

it is and doesn't like that guy or wants to send a message and then like two women down says like that was a 10 that was incredible and that is like a known version of conflicts I would say yeah this is so fun yeah um so then so I did this and I would say this is really treating the data as way simpler than it is so this is acting as though it's like a perfect round robin everyone's interacting with each other, which they're not because the men aren't kissing the men and the women aren't kissing the women. And this is already getting rid of the many, many seasons where only the men or only the women do the kissing. So that's a bummer in terms of how much data we actually have available. And I think there's probably a way to estimate those kinds of seasons as well, but I have not figured out what it is yet because technically they're not very reciprocal but for these seasons where the men did the kissing and then the women also did the kissing so we have scores on both

sides what it actually is design wise is an asymmetric block design which is basically just where people are interacting with each other but they're there within their own in group and they're only interacting with people of the out group. And so that you can estimate I think more appropriately with like a mixed effect model where you also then incorporate group so season in this case And if you doing a mixed effects model what really fun is then you can start incorporating gender to see if, like, are the men behaving differently than the women? Because I would say, like, behaviorally, the men are behaving very differently than the women. They're, like, often crawling on top of each other and, like, high-fiving and having a really good time about how their buddies are really kissing these girls that they all like. The women are usually just kind of upset. So it's an interesting dynamic. But then when we look at the variance components, there's not really much difference at all.

The actor variance looks slightly different, but it's so minimal regardless, that kind of across the men's scores, the women's scores, and overall scores, that partner variance or the person doing the kissing always accounts for somewhere between 20 and 30 percent of the variance and then the relationship variance always accounts for somewhere between like 70 75 percent of the variance an actor makes up the rest and it's pretty tiny yeah that's so interesting so but that sort of so the partner is just so to me that suggests that people are somewhat behaving consistently for the same partners right like it like they are if there's very little actor variance that would mean that like the not necessarily the scores themselves but the variation in the scores is not differing that much between actors so people might all have their own scale like i might like only range between a two and a

And as we know about Sarah, she's always going to be in the 8, 9, or 10, the way she rates books. I was going to say, I don't know how I would rate a line of men. But it is true that at least on, like, Goodreads, I feel high. Okay, this is true. I don't think it's very about how you rate Goodreads. I don't know. Do you think so? Yeah, tell me. But their variants, right? Am I interpreting this correctly, that their variants seems to be consistent? There's not really actor variance effects that we're witnessing here. That's my interpretation as well. It's essentially like there aren't, not only is there not a lot of variance in the actor, but like none of the actors are, none of the people judging Kisses are wildly different from each other as well. Yeah. Because we're not seeing that as like a significant effect. So everyone is, for the most part, scoring within that same kind of band, which is usually between like seven and nine. they're giving each other pretty high scores

and then there's a few of those kind of outliers where you can see, oh, there's a very clear social dynamic happening here, which is why she's giving him a two or things like that. Yeah. Okay. Fascinating. And that would show up, right? That would show up in the relationship if it was like... Yes, it should. If all is going as planned. Yes. It's a big if, but it could happen. So because the relationship in Arrow and Arians is so big, I was struck with like, ugh, wouldn't it be so cool if we could see how these things are related? And because we have these two seasons where everyone kissed each other, all the men kissed all the women and all the women kissed all the men, what I was able to do is actually make a bigger merge data set where each row, instead of being one kiss, we're going to talk about emoji plots. plot as well. I love this emoji plot. I went through a real emoji plot era in my grad school

days. I want to know all the details. This is emojiji. Emojiji. Big fan. Yeah. Emojiji. This is incredible. Yeah. I'm sorry I interrupted. No you're so fine. So what I did is I made each row into like a couple. So rather than just being one kiss each row is a couple and then I have the man score for when the woman was kissing him and the woman's score for when the man was kissing him so the scores don't represent the same kiss i wish they did but they do represent each person being the actor and being the partner so this is a plot of how those scores relate to each other as a way of starting to think about that relationship effect it's not a perfect estimation of it but they are correlated and you can see like yeah when when one woman scores men high or scores a man higher that man also tends to score her higher so there is something going on where

people are generally pretty reciprocal with each other which for frm terms would be called like dyadic reciprocity i like that even this poor little pairing in the bottom left yeah it seems two have also been reciprocal but it's funny that like as mean as the women get like the low score there's these scores are about a five the men are like no that's a two and a zero like the men are so much meaner yeah on this particular example yep but it does stand out so much versus like basically beyond that the men are like it feels like they're all i guess it's four and up but it does seem like the majority are like six and higher like you're saying versus the women have like this wider range yeah and i think a lot of that is also somewhat the dynamics on the show like i don't know i'm biased off the most recent season of love island where the women like really banded together against men being annoying uh and in that it was very much like how dare the men

ever do this kind of mean thing to us but like as women it's totally fine if we're kind of mean to them right so that dynamic kind of persists here where you see there's a bunch of women who are like i feel totally comfortable giving a six because that was kind of a mediocre kiss but then the men are still giving them like an eight even up to like i think there's one that gives a 10 so like who knows yeah yeah is there a time difference so like i know you said it's not the same kiss but is it the same episode okay so there's all wondering could there be like a falling out if you do like a kiss on episode one and a kiss again on episode three and it's okay i was like that feels like that's how we'd end up with these like really aggressive kind of opposites of like a 10 and a zero or a zero and a 10 yeah no it this one it's all in one block which this is the problem is what I want to say to Love Island producers is like please keep doing these where the men and the women are both the kissers and also maybe do multiple kisses and let them rank

them all and then I went back and I watched just two seasons worth of kissing challenge scenes and I was like this is a ridiculous amount of kisses I don't want to be watching this for this long like it's bad television so I can't rightly ask for that but that is what I want data west how did you did you manually you like took you watched it and just recorded no thankfully I was going to do that and then I said let me just check and see if this fan wiki has it and thank god for people on fan wiki because it's everywhere I think this is the third or fourth episode with a fan wiki shout out. Yes. I think our Law and Order data came from there. My severance transcripts came from a fan wiki, although I also had some manual. Yeah. My scandal survival, which we haven't talked about on here, but was like how long until Shonda Rhimes kills characters off in Scandal? Also from the wiki. Amazing. Yeah. Okay, I love this. So, yes,

does look like positive correlation and also like hilarious mismatches occasionally where young people Can I ask as a presumptive, we do a little reviewer 2-bit later, but in the rules of the game, does one couple win? One woman and one man. But not necessarily having been coupled. No. Okay. Because I was like, I'd love to see, like, highlighted in, like, a different, like, which one of these won. But that's so interesting. So you win for, like, your independent merit. You win for your high score. And all you win is, like, bragging rights. So, yeah. Yeah. Yeah. And I would say also, like, there is a, there are ways that people can socially win this game, even if they don't win, like, the score. Like, you can, for instance, just give a really good kiss to your couple partner and then give, like, really mediocre kisses to everyone else. And I think more people in the game would be like, yeah, that's so responsible of you.

Great job. You're such a, like, nice partner. And that is, I think, a greater win in the context of the game. Like, no one ever goes back and says, like, can't believe she got 40 points in the kissing challenge. Incredible. Not super much a thing, yeah. What I do have in terms of manual variables and highlighting specific things is I went through, because it was only two seasons, I did this manually because I didn't feel like figuring it out. And I marked everyone who was ever in a couple. Amazing. Throughout the whole season. So good. And look at that zero. Yes. This is what I wanted to know. Yeah. And still, she's like, he's a five. Yeah. It's fine. Yeah. Yeah. So, yeah, you can see, like, the people who were in a couple either at this point or end up in a couple at some point.

Almost all of them score way higher for each other. And then you have this one that's having a fight and are upset with each other. And so they're giving each other the lowest possible scores they can imagine, which for a man is a zero and for a man is a five. like there's all kinds of things you could ask about that yeah yeah what was I gonna say oh and for this I was I originally did if they were in a couple like at the time that they kissed and that was like marginally significant as a fixed effect and didn't look nearly as convincing on the graph. And then I went back and I was actually like remembering some of the plot points. And there's plenty of people where they're not coupled up right then because, say, this bombshell has just entered the villa, so they haven't had a chance to couple up with their person yet,

but they couple up the very next day. Or, you know, this couple's in the process of breaking up, like this one that we see that's scored really low, is in the process of breaking up, But then she's going to get with someone else and she's going to score him really high. So I went through and changed it from being a couple at that time to being a couple all over the whole season, which was less. There was less flopping around than I remembered anecdotally from watching the show. I was like, wow, these people stay in their couples kind of consistently, which is a whole nother fun analysis that someone could definitely do. Yeah. And then I also did a fixed effect. This is my last plot. I said I included a fixed effect of that couple status. And it's significant. There was no significant interaction between men and women and their couple status But if you look at this figure there a bigger gap for women between the scores for men they are never in a couple with and men they are in a couple with whereas

men are approaching more similarity between women they're not in a couple with and women they might ever be in a couple with yeah so it looks like right so like women it's like a seven and a half on average for non-couples and an eight and a half for couples whereas men it's like what is at like 7.75 versus 8.1 maybe yeah like yeah that those are I do I think I yeah I can see I can see what you're saying yeah this is great so and like practically so these are just fit again you use like there's a random effect for a person for kiss or a random effect for kissy and then you just put in a fixed effect for like for gender couple gender couple status and then interaction between the two or sort of so this one um with the asymmetric block design i ran using some code there's a paper that came out last year specifically on using an asymmetric

block design okay and doing that analysis in r so it's a bit more complicated than that where they have some there's there's an additional contrast code for if it's a man kissing a woman or a woman kissing a man as a fixed effect so we can see those general differences and then they add in basically like each instead of just having an actor effect and a partner effect you have those for women kissing men and men kissing women you basically separate out those actors so there's like three different random effects three four or maybe four i can't remember their code is very clearly laid out and very easy three i could see three because one would be the like if it's an indicator like the one would maybe be completely contained in the other three i think i could see yeah it being yeah that makes sense that okay i love this that was fun great yeah and i love it's so interesting Sarah I feel like are we Sarah and I both are biased statisticians by training

and like a lot of these so are not most recent but second to most two episodes ago we had Matan on talking about this marshmallow test and he was talking about like he used a triangle test and then he also which I it was basically like a way to do I guess it's used a lot in food science or someone commented on Blue Sky to say they also use a similar kind of testing and like audio for audio detection. But it's like you have – there's two things you're trying to see if people can distinguish between. So you give them three where two are the same and one is different, and you just ask them to identify which one is different. Yep. So they stay like – they can remain blinded, and you also can like make sure – I guess it's sort of like a self-control a little bit for like, you know, you're not having – and you're not having to identify which is which. So it's not like they don't have to, in that construct, they don't have to say which is which. They can just say which. They can just see if they can detect the difference. So I had never heard of this, and I feel like it's, and then he was telling us about these, like, signal-to-noise models that, like, it was just like a GLM with a probit link, which, again, is, like, something that we talk about in Biosda.

And I guess, like, afterwards, I was talking to one of our colleagues, Stacy, who does a lot of Bayesian inference, and she was telling me they always use probit links in most of what she's doing just, like, for convenience. But I, like, had never heard of these applications. And it's the same. I mean, we use a lot of mixed effects models. They're, like, I feel like the bread and butter of most of what we do in Biostats because we always have repeated measures. But I've never heard of this type of, you know, I guess because our data doesn't often look like this. But this is, it's so cool to hear about these, like, other ways of using the same statistical techniques to answer, like, different questions. And even just, like, the interpretation of what the different coefficients mean under whatever paradigm. It's so cool. I was just going to say, like, part of what's so helpful about this paper from last year about running this kind of code is less so the actual model itself. Like, it helps you build it, and that's great. But they also have all the supplementary material of various tabulation functions because so much of it is you can get the standard output from the mix effects model.

But what you actually want is the variance estimates and then you want them standardized within the amount of variance. It's in the whole thing. And they have written all of that. So you can just run the one line and you get your beautiful little table and it has all the things. and it's similarly I had never worked with like transforming any of those outputs into anything like this and it's like oh my gosh this is so much easier I don't have to do any of the crazy math I don't have to figure out like what any of it means they can actually just transfer it which is really just a lovely lovely component yes I think that the distinction Lucy too is like We both do a lot with like missing data and measurement error, but we don't, or at least I don't often live in a space where things are truly latent. Like the idea of like that relationship spark, it is not directly measurable. It's a latent characteristic or like an abstract construct. And I feel like that's something we, we usually have it for some people. We don't have it for everybody, but we have it for some.

And when you get into this space where it's like we acknowledge that it exists, but we have it for no one. That is also a lot of the time like models that were used to it used in a different way. So I am learning like like factor analysis for a paper on like alcohol and substance use where alcohol use is a latent construct that you're trying to capture from like this audit. It's like a 10 question inventory of different behaviors. And I was reading papers in different journals. And at the end of the day, I was like, oh, this is just a linear regression with a latent covariate. But it is funny to come across where it's like, mathematically, we could do that, but I hadn't encountered a reason to do it before. But I do think there is, I don't know. I don't know, Hannah. Have you ever done a factor analysis? Because that was the other thing I wondered. I was like, do you have these scores and could you treat them as like being the end, like being the result of that relationship spark and use it as a different way of modeling that piece? So I think you could. I've done, I would dabble in factor analysis.

in a course that I took a few years ago. So not confident in it at all. Me either. I think the issue that you run into is there's so much of this like specific, like there is some level of partner specific behavior. Like you do have people who are just better at kissing and worse at kissing. And so you would also need to capture that as well, because otherwise it would kind of start to cancel out some of that relationship effect and you'd say like, oh, this person is just consistently bad. Yeah. I also just think this, I think with this amount of data, it would be nothing because there's like no data at all, which is part of the, like, I'm a lot less familiar with some of these things because I work with child language data where, like, you're very lucky if you have 40 kids. That'd be incredible. And you're so lucky if 30 of them talk. And so you just don't have the number of data points that you need to do those kinds of analyses, which is always kind of a bummer.

It's the reality, though. I get it. Yeah. It's also so refreshing to hear about like small and like real small end scenarios, because I feel like stats, like we have so many beautiful methods for small end scenarios that require like thinking. It's like it requires our expertise in a way that I feel like the large end scenario. I mean, it's not to say you can't have bias in these large end scenarios, but I think the large incineraries offer more opportunities for kind of throwing an algorithm and letting, or throwing a suite of algorithms and letting them just sort of like sort out what they can make from it. And you like can't do that. If you have 30 observations, you can't do that because you won't get anything meaningful. You'll mostly just be fitting to noise like it. And so I think I love hearing about like examples where N is small. So we still need, we're still needed. Our discipline is still important. yeah and I should add with SRM you can actually do you can have the outcome kind of like go to a

latent construct you can put multiple outcome scores into that like what you're regressing on which is kind of nice if you have multiple scores so there's a lot of really fun papers out there that do like this example paper was combining like people's attractiveness ratings and people's sexiness ratings and then saying if that makes them go on another date um and so you can do things like that where you're kind of combining those two scores into sort of a latent construct yeah but again you really have to think about like okay which thing is leading to what and what am I actually asking um it gets really messy with the like who's the actor and who's the partner depending on what you're doing like even with this stuff I feel like I have to keep being like okay the kissy is the one doing this and the kisser is the one doing this and it just gets mucky yeah this is so fun well this has been excellent I we so usually I well I think we've already kind of like gone through some of the reviewer too Sarah had some some points there and the last

thing we usually do is this fetch rating we try to have you rate your own analysis on a scale which I was actually going back and listening and realized some of the more recent episodes we've claimed that the scale is one to five fetches but I actually think with someone like I think maybe with emily we didn't give her a max like we just were like yes like it we were like it's just someone say how many touches well so matan described himself as fetch maxing which i love yes yes he took the the hat the top so anyways yeah you can pick it up about i mean it might be festive to give a max of 10 fetches that's what i was gonna say yeah to agree with the given yeah yeah yeah okay perfect like 7.5 to 8 and I think a lot of that is that I wish there was more data and more people were doing more full round robin kissing on these shows that's my that's my big soapbox if I have to stand on one from this you want it you would like for it to exist for the data you don't want to watch it but I don't want to watch it yeah but if the fans could put it on

the fan wiki that would be yeah if they want to go to a full round robin where we do the whole interpersonal issues of like all the men also have to kiss all the men and all the women also have to kiss all the women i would absolutely watch a full episode of that i think that would be fascinating but if it's just going to be men and women just kissing multiple times i think that could be a behind the scenes but then give us just give us the data yeah just just show us that little that little that little whatever the the table that's all i need yeah oh that's so good okay 7.5 fetches i think that's the most fetches we've had so this is excellent although i mean i don't know we haven't always yeah i love it this is that we we created no real good metric on this and so everything is good that's the beauty you know it's the beauty yes yes well this was so awesome. I think it's also a good opportunity to remind people that we do have a Gmail account. If you, like Hannah, have a really cool data side quest that you'd like to share,

you can email us at regressiontothemeangirls at gmail.com. Thank you so much for joining us. You go again, Coco. We are Regression to the Mean Girls. We're mean as an average, but actually very nice. Tune in next time.