I take adjective "multivariate" to mean that there are multiple (often to be taken as "more than two") statistically dependent variables in the full joint distribution for the collection of variables being considered. This definitional approach mostly agrees with what people more broadly call "multivariate analysis" which might include MAN(C)OVA, GLM, PCA, factor analysis, CCA, CA, PCoA, discriminant analysis (e.g. LDA), clustering, recursive partitioning, ANNs, parallel coordinate plots, simultaneous equations, vector autoregression, and many others. But it does disagree with people who say that "multivariate regression" merely means multiple predicted variables as my view allows for further statistical dependence among the predictors. I've even seen people say that you cannot perform regression when there are statistically dependent predictors (often citing perfect multicollinearity or variance inflation). But I don't agree with that at all. Often what is required in my experience is to include a latent covariance matrix over those variables.
If you're going to plot integer-valued data using a histogram, I recommend taking care to set the bin widths to unity and decide whether you want the bin boundaries to be left/right/center-located.
9:35 One reasoning I heard from a statistician for why it's often not an interaction if the lines don't cross is that it can usually be transformed away
I've never taught an introduction to categorical variables, but I expect that the visualization of "drawing a slope" helps students see that this is part of the space of linear models. It is metaphorical as there are no intermediate values in the data between the two levels of a binary (categorical) variable.
One thing I would like to do more of is use colour palettes in my plots that are still distinguishable to people with colour blindness. Using different line and marker styles also helps.
Your last example is essentially a mediation or a moderation effect correct? and a 4 way interaction, or changing variable D alters the the effect of variable A, on variable B, in the presence of variable C. Which is essentially a moderated-mediation effect.
thanks a bunch!! I have a random question: how to add a proportional weightage to a numeric variable on the outcome variable in a lm/glm and visualise, it is much like giving the weightage to the sample size of each study “n” to the outcome. Much like meta analysis. thanks in advance.
What precisely is meant by "curvilinearity" in this video? Just a synonym for a model which is nonlinear in its predictors? The examples of log transform and polynomial predictors in the recent video are still just linear models in the conventional sense of being linear in the parameters. That would seem to match.
N-way interaction effects can be well-understood through a combination of pure mathematics and simulation experiments. I don't tend to find them completely on their own, but if you do then they should tend to maximize the 'multilinear' product-moment correlation coefficient that I developed in my MSc thesis (section 3.1 if I recall correctly). These days I feel Luke-warm about the correlation functions I defined, but my discussion of parity, signum and orthants might provide some intuition.
Lines and line segments are not actually the same thing, Colloquially it is fine to call a line segment a line, but when careful reasoning is required I think that conflating these terms can create confusion. Despite the word "line" in "line segment", line segments are not lines and they are not linear due to their end points. Lines by definition must go on forever in both directions. You have thousands of years of geometry to thank for that. If I recall correctly, Euclid was the first mathematician to axiomatize Euclidean geometry. Among those axioms is the parallel postulate. Interestingly, rejecting the parallel postulate leads for elliptic and hyperbolic geometry. And just before you think that's just math trivia, both of these non-Euclidean geometries are used in Physics. And if you think that's weird, wait till you see pseudo-Riemannian manifolds.
you could make up a better word to replace "multivariate" for multiple predictors then it gets a wikipedia entry and you get one for inventing it *plus one for marginal plots; why not
My experience with Wikipedia is that the term would usually need to be somewhat accepted by a community of people 'before' moderators would allow such a Wikipedia page to exist.
I should :). Maybe just a "dustin" analysis. "Oh, I see you have multiple predictor variables. Have you ever taken a dustin class? You need to use a dustin analysis for this."
Not specifically that. My approach is to analyze it as is, then analyze it with the outlier deleted and see if it matters. If it doesn't matter, I don't have to worry about it. If it does, I report the results of both approaches.
@@QuantPsych exactly, the 2 random factors are categorical. Additionally, one of the predictors of the 3-way interaction term is numerical. Ideally, it should be the x axis and plot the trends. So far, I am using emtrends.
Some of this approach seems to assume that if you have evidence of non-linearity in the predicted variable (as a function of the predictors) that it is presumably from an interaction effect. While interaction effects are non-linear (specifically multilinear), they are just one of an infinite number of ways for something to be non-linear. If I were to say that a non-linearity isn't an interaction effect it would be like saying that something isn't a banana; it doesn't narrow it down very much. I think that interaction effects are worth considering, but when I see evidence of non-linearity I ask a broader question about what form of non-linearity rather than defaulting to the assumption of an interaction effect.
I see why you're saying that, but that's not what I meant. In retrospect, i should have clarified that a bit. If you read the paper it's more clear why you're looking for nonlinear effects.
when looking at the intercepts to see if there's a main effect, shouldn't we mean center things? Even the smallest change in slope can have big differences in the intercept if our X range is quite large instead of closer to zero. I love geeking out about stats, but nobody else I know does :(
Unless I'm missing something, I don't see how that will change anything. The axis labels will change, but the angle of the slopes won't. See the R code below (if youtube will allow me to post it??). require(tidyverse) require(flexplot) a = matrix(.4, nrow=3, ncol=3); diag(a) = 1 a = fifer::cor2cov(a, c(5,5,5)) d = MASS::mvrnorm(n=555, mu=c(50,50,50), Sigma = a) %>% data.frame %>% set_names(c("y", "x1", "x2")) flexplot(y~x1 + x2, data=d, method="lm") flexplot(y~x1 + x2, data=d %>% mutate(across(everything(), scale)), method="lm")
@@QuantPsych I'm getting a error when I try to install your fifer package. Welp, that means I need to sign up for your simplistics R course. I know just enough R to be dangerous and chatGPT has made me very dangerous with R. Time to learn R for realz...I was wanting to hold off until I had my latest R&R back at the journal and my current paper submitted before pulling that trigger.
![Kodak Black - Versatile 4 [Official Video]](http://i.ytimg.com/vi/VcP_1Ua__vY/mqdefault.jpg)
I take adjective "multivariate" to mean that there are multiple (often to be taken as "more than two") statistically dependent variables in the full joint distribution for the collection of variables being considered. This definitional approach mostly agrees with what people more broadly call "multivariate analysis" which might include MAN(C)OVA, GLM, PCA, factor analysis, CCA, CA, PCoA, discriminant analysis (e.g. LDA), clustering, recursive partitioning, ANNs, parallel coordinate plots, simultaneous equations, vector autoregression, and many others.
But it does disagree with people who say that "multivariate regression" merely means multiple predicted variables as my view allows for further statistical dependence among the predictors. I've even seen people say that you cannot perform regression when there are statistically dependent predictors (often citing perfect multicollinearity or variance inflation). But I don't agree with that at all. Often what is required in my experience is to include a latent covariance matrix over those variables.
If you're going to plot integer-valued data using a histogram, I recommend taking care to set the bin widths to unity and decide whether you want the bin boundaries to be left/right/center-located.
9:35 One reasoning I heard from a statistician for why it's often not an interaction if the lines don't cross is that it can usually be transformed away
I've never taught an introduction to categorical variables, but I expect that the visualization of "drawing a slope" helps students see that this is part of the space of linear models. It is metaphorical as there are no intermediate values in the data between the two levels of a binary (categorical) variable.
Thank you for the Visual Partitions article!! :)
Of course!
One thing I would like to do more of is use colour palettes in my plots that are still distinguishable to people with colour blindness. Using different line and marker styles also helps.
The marginal plots are a neat idea.
Your last example is essentially a mediation or a moderation effect correct?
and a 4 way interaction, or changing variable D alters the the effect of variable A, on variable B, in the presence of variable C. Which is essentially a moderated-mediation effect.
thanks a bunch!! I have a random question: how to add a proportional weightage to a numeric variable on the outcome variable in a lm/glm and visualise, it is much like giving the weightage to the sample size of each study “n” to the outcome. Much like meta analysis. thanks in advance.
Good too see some new stuff coming up,
Very well done with the three-way interaction. I currently have to deal with it 😢
These videos are not for the first-timers. Cool for those who already know how to chat about statistics.❤
Alas, this is true.
What precisely is meant by "curvilinearity" in this video? Just a synonym for a model which is nonlinear in its predictors?
The examples of log transform and polynomial predictors in the recent video are still just linear models in the conventional sense of being linear in the parameters. That would seem to match.
N-way interaction effects can be well-understood through a combination of pure mathematics and simulation experiments.
I don't tend to find them completely on their own, but if you do then they should tend to maximize the 'multilinear' product-moment correlation coefficient that I developed in my MSc thesis (section 3.1 if I recall correctly). These days I feel Luke-warm about the correlation functions I defined, but my discussion of parity, signum and orthants might provide some intuition.
Lines and line segments are not actually the same thing, Colloquially it is fine to call a line segment a line, but when careful reasoning is required I think that conflating these terms can create confusion. Despite the word "line" in "line segment", line segments are not lines and they are not linear due to their end points.
Lines by definition must go on forever in both directions. You have thousands of years of geometry to thank for that. If I recall correctly, Euclid was the first mathematician to axiomatize Euclidean geometry. Among those axioms is the parallel postulate. Interestingly, rejecting the parallel postulate leads for elliptic and hyperbolic geometry. And just before you think that's just math trivia, both of these non-Euclidean geometries are used in Physics. And if you think that's weird, wait till you see pseudo-Riemannian manifolds.
you could make up a better word to replace "multivariate" for multiple predictors
then it gets a wikipedia entry and you get one for inventing it
*plus one for marginal plots; why not
My experience with Wikipedia is that the term would usually need to be somewhat accepted by a community of people 'before' moderators would allow such a Wikipedia page to exist.
I should :). Maybe just a "dustin" analysis. "Oh, I see you have multiple predictor variables. Have you ever taken a dustin class? You need to use a dustin analysis for this."
Hi
Thank you for all your videos.
Do you have a video explaining how to handle Outliners? (e.g., omit zscore >3?, IQR *1.5 and etc)
Not specifically that. My approach is to analyze it as is, then analyze it with the outlier deleted and see if it matters. If it doesn't matter, I don't have to worry about it. If it does, I report the results of both approaches.
Hey can you do a video explaining the dispformula in glmmTMB? Thanks ahead of time.
Looking forward to watching the second part! How could I plot a 3-way interaction model with flexplot if I have two random factors?
Meaning two categorical variables? The same way you would with two numeric variables.
@@QuantPsych exactly, the 2 random factors are categorical. Additionally, one of the predictors of the 3-way interaction term is numerical. Ideally, it should be the x axis and plot the trends. So far, I am using emtrends.
Some of this approach seems to assume that if you have evidence of non-linearity in the predicted variable (as a function of the predictors) that it is presumably from an interaction effect. While interaction effects are non-linear (specifically multilinear), they are just one of an infinite number of ways for something to be non-linear. If I were to say that a non-linearity isn't an interaction effect it would be like saying that something isn't a banana; it doesn't narrow it down very much. I think that interaction effects are worth considering, but when I see evidence of non-linearity I ask a broader question about what form of non-linearity rather than defaulting to the assumption of an interaction effect.
I see why you're saying that, but that's not what I meant. In retrospect, i should have clarified that a bit. If you read the paper it's more clear why you're looking for nonlinear effects.
Fair enough.
Love the videos! request for a future video about moderation mediation analysis in R? :)
I'll add it to my list :)
really enjoy the video, thanks!
when looking at the intercepts to see if there's a main effect, shouldn't we mean center things? Even the smallest change in slope can have big differences in the intercept if our X range is quite large instead of closer to zero. I love geeking out about stats, but nobody else I know does :(
Unless I'm missing something, I don't see how that will change anything. The axis labels will change, but the angle of the slopes won't. See the R code below (if youtube will allow me to post it??).
require(tidyverse)
require(flexplot)
a = matrix(.4, nrow=3, ncol=3); diag(a) = 1
a = fifer::cor2cov(a, c(5,5,5))
d = MASS::mvrnorm(n=555, mu=c(50,50,50), Sigma = a) %>% data.frame %>% set_names(c("y", "x1", "x2"))
flexplot(y~x1 + x2, data=d, method="lm")
flexplot(y~x1 + x2, data=d %>% mutate(across(everything(), scale)), method="lm")
@@QuantPsych I'm getting a error when I try to install your fifer package. Welp, that means I need to sign up for your simplistics R course. I know just enough R to be dangerous and chatGPT has made me very dangerous with R. Time to learn R for realz...I was wanting to hold off until I had my latest R&R back at the journal and my current paper submitted before pulling that trigger.
@@zimmejoc I think you're coming to a reasonable conclusion that ChatGPT is not really a substitution for knowing how to code.
Oh thanks you comebackk still waaiting your make tutorial on latent varoable modeling, factor analysis, pca optimal scaling, sem, irt as glmm, dcm etc
I'll put them on my list :)
this is great
Goated
I really like these videos but the background music is distracting sadly :(
Yay!
Double yay!