Prompted by new data from our weekly polling with YouGov, I shared a graph of the growing gender gap in American politics yesterday:. The gender gap in the generic ballot grew from 35 to 45 pts!! Seems to be corresponding with a better overall generic ballot for Democrats. It is not a good long-term strategy to tick off suburban women. The growing divide in the preference for Democrats over Republicans among men versus women — here shown among only college-educated Americans — is a striking development in US politics.
An electorate divided as deeply by gender as other demographics, like educational attainment or race, would certainly push us into uncharted territory.
LOESS smoothing, short for local regression and akin to locally weighted scatterplot smoothing, or LOWESSis a form of nonparametric regression that can be used to uncover and explore nonlinear trends in data. However, they are not always the optimal pick. As people shared with me after I posted the original graph, LOESS smoothing might be an imperfect representation of trends and uncertainty in polling data.
Allow me to be clear in saying that there is no single answer for which technique is best. Here, I compare my typical LOESS approach with a much more sophisticated one: a Bayesian implementation of generalized additive models.
The default standard deviation used for this model is 0. The other arguments are ones passed to stan. And if we draw from the predictive posterior distribution, we see that the equation does a rather good job of predicting the data — if not a little too uncertain notice the fat tails of y-rep. Ultimately, what we want is a plot that looks similar to the original but draws its trend based off the Bayesian GAM. Here is the ggplot2 code to make the plot, which graphs the GAM smooth with a filled line and colored fill alongside a LOESS trend, with a dotted line and grey fill for either gender.
This could be due to the relatively high standard deviation of the brms equation, or to the the short default span of the LOESS. Wickham, Hadley. Ggplot2: Elegant Graphics for Data Analysis.
Springer-Verlag New York. Next steps: Dynamic standard error in the model: right now, I use the same standard error of the y variable at every point for the x.
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This part of the trend-fitting is very much in progress. If you have an idea of how to solve this problem, ping me! Make more trends! Like for voter turnout.It can be hard to view trends with just points alone. Many times we wish to add a smoothing line in order to see what the trends look like. This can be especially helpful when trying to understand regressions. Again, the smoothing line comes after our points which means it is another layer added onto our graph:. Note what happens as you slowly build these layers.
This is a major part of the power of ggplot2.
Difference between gam() and loess().
We have so far just seen how to add the smooth without being able to do anything but add or subtract the confidence bands. We now will change the smoothness of our smooth that we added. The span can be varied from 0 to 1, where 0 is very rough and 1 is very smooth.
Loess smoothing is a process by which many statistical softwares do smoothing. In ggplot2 this should be done when you have less than points, otherwise it can be time consuming. It works with a large number of points.
Previous module:. Smoothing It can be hard to view trends with just points alone. Varying the Smooth We have so far just seen how to add the smooth without being able to do anything but add or subtract the confidence bands. Different Types of Smooths There are different types of smooths that we can do. We will consider: loess gam Loess Smooths Loess smoothing is a process by which many statistical softwares do smoothing.Search everywhere only in this topic. Advanced Search. Classic List Threaded.
Difference between gam and loess. Most noticeable at the endpoints of the range of x. Can anyone enlighten me about the reason for this difference? Kevin E. Re: Difference between gam and loess. Ravi Varadhan. Good try, Kevin. But that doesn't seem to do it. I looked at the Fortran codes from both loess and gam. They are daunting, to say the least. They are dense, and there are absolutely no comments whatsoever. But one thing is clear - they are using different Fortran codes.
So, the best bet might be to get Trevor Hastie or Bill Cleveland to help you out. Is it important that these two results be identical? Best, Ravi. In reply to this post by Ravi Varadhan. Thanks for doing this digging. There are two obvious differences in the defaults. Kevin -- Kevin E. In loess. I would think that could also account for tail departures especially. I don't gave the gam package installed, so can't test these myself at the moment.
Somehow when I read the above Ravi, I missed that you had fiddled with loess. I guess one simple parameter change may not quite do it. Free forum by Nabble. Edit this page.A smoother in gam separates out the parametric part of the fit from the non-parametric part. For local regression, the parametric part of the fit is specified by the particular polynomial being fit locally. The workhorse function gam. All the parametric pieces from all the terms in the additive model are fit simultaneously in one operation for each loop of the backfitting algorithm.
Any dimensional argument is allowed, but typically one or two vectors are used in practice. The matrix is endowed with a number of attributes; the matrix itself is used in the construction of the model matrix, while the attributes are needed for the backfitting algorithms all. Local-linear curve or surface fits reproduce linear responses, while local-quadratic fits reproduce quadratic curves or surfaces. These parts of the loess fit are computed exactly together with the other parametric linear parts Note that lo itself does no smoothing; it simply sets things up for gam ; gam.
One important attribute is named call. For example, lo x has a call component gam. This is an expression that gets evaluated repeatedly in all. When gam. Hastie, T. Chapter 7 of Statistical Models in S eds J. Chambers and T. London: Chapman and Hall. If it is a list of vectors, they must all have the same length. This is the smoothing parameter for a loess fit. These are also the variables that receive linear coefficients in the GAM fit.
It only takes a minute to sign up. I gather GAM stands for generalized additive models and it uses a cubic spline. Splines are approximations that connect different piecewise functions that fit the data which make up the generalized additive modeland cubic splines are the specific type of spline used here. What matters the most is the number of effective degrees of freedom that you give to each approach. For nonparametric smoothers such as loess this is controlled by the bandwidth whereas for regression splines the d.
Splines are more general in the sense that they can be used in a greater variety of contexts. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Asked 4 years, 9 months ago. Active 4 years, 9 months ago. Viewed 5k times. Are the following perceptions correct?
Loess estimates the response at specific values. Andrew Marderstein Andrew Marderstein 2 2 silver badges 9 9 bronze badges. Active Oldest Votes. Frank Harrell Frank Harrell Sign up or log in Sign up using Google. Sign up using Facebook.Our matched betting tips provide the latest team news with details of injuries and suspensions plus predictions on how the competitors will line up. No betting preview is complete without odds and our matched betting tips include the best odds to help you find the best value for money.
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Rcode: Loess and GAM
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COM PSG: Ibrahimovic confirms the interest from the Premier League. Lesson Goal: To understand the difference between an observation, inference and prediction. You will be able to check your answers.