I plot the components of FB Prophet model forecast, but I do not know how to well explain the plots.It output "trend","holidays","weekly" and "extra_regressors_multiplicative" line charts.
What do those figures indicate? Thanks a lot!
They are all one of the components of the additive (or multiplicative) model (y(t) = g(t) + s(t) + h(t) + ϵₜ) which is Prophet :
g(t) models trend
s(t) models seasonality
h(t) models the effects of holidays or large events
ϵₜ is the error term
You can think of the seasonality as, for each day, the change from what y would be if there were no seasonality at all.
For instance if the effect of a certain holiday (like Christmas) is +20 (units), it means y(t) would have been 20 units less if it wasn't Christmas.
Related
I have generated a Kaplan Meier survival curve on the consumer data (the event of interest is 'Churn'). I have the survival curve for both buyers and nonbuyers. Before jumping into the use of the model. I want to know how I can evaluate the truthness of the curve?
I have already tried creating a separate curve for the two different consumers cohorts (who joined in a different year) for the span of 36 months. I noticed that these curves are not similar at all. I believe this is not the right way to evaluate. Can somebody tell me what can be tried to evaluate the survival curve apart from the statistical methods?
I saw a lot of tutorials online on how to use polynomial regression on Excel and multi-regression but none which explain how to deal with multiple variable AND multiple regression.
In , the left columns contain all my variables X1,X2,X3,X4 (say they are features of a car), and Y1 is the price of the car I am looking for.
I got about 5000 lines of data that I got from running a model with various values of X1,X2,X3,X4 and I am looking to make a regression so that I can get a best estimate of my model without having to run it (saving me valuable computing time).
So far I've managed to do multiple linear regression using the Data Analysis pack in Excel, just by using the X1,X2,X3,X4. I noticed however that the regression looks very messy and inaccurate in places, which is due to the fact that my variables X1,X2,X3,X4, affect my output Y1 non-linearly.
I had a look online and to add polynomials to the mix, tutorial suggest adding a X^2 column. But when I do that (see right part of the chart) my regression is much much worse than when I use linear fits.
I know that polynomials, can over-fit the data, but I though that using a quadratic form was safe since the regression would only have to return a coefficient of 0 to ignore any excess polynomial orders.
Any help would be very welcome,
For info I get an adujsted-R^2 of 0.91 for linear fits and 0.66 when I add a few X^2 columns.
So far this is the best regression I can get (black line is 1:1):
As you can see I would like to increase the fit for the bottom left part and top right parts of the curve.
I've got files with irradiance data measured every minute 24 hours a day.
So if there is a day without any clouds on the sky the data shows a nice continuous bell curves.
When looking for a day without any clouds in the data I always plotted month after month with gnuplot and checked for nice bell curves.
I was wondering If there's a python way to check, if the Irradiance measurements form a continuos bell curve.
Don't know if the question is too vague but I'm simply looking for some ideas on that quest :-)
For a normal distribution, there are normality tests.
In short, we abuse some knowledge we have of what normal distributions look like to identify them.
The kurtosis of any normal distribution is 3. Compute the kurtosis of your data and it should be close to 3.
The skewness of a normal distribution is zero, so your data should have a skewness close to zero
More generally, you could compute a reference distribution and use a Bregman Divergence, to assess the difference (divergence) between the distributions. bin your data, create a histogram, and start with Jensen-Shannon divergence.
With the divergence approach, you can compare to an arbitrary distribution. You might record a thousand sunny days and check if the divergence between the sunny day and your measured day is below some threshold.
Just to complement the given answer with a code example: one can use a Kolmogorov-Smirnov test to obtain a measure for the "distance" between two distributions. SciPy offers a neat interface for this, called kstest:
from scipy import stats
import numpy as np
data = np.random.normal(size=100) # Our (synthetic) dataset
D, p = stats.kstest(data, "norm") # Perform a one-sided Kolmogorov-Smirnov test
In the above example, D denotes the distance between our data and a Gaussian normal (norm) distribution (smaller is better), and p denotes the corresponding p-value. Other distributions can be similarly tested by substituting norm with those implemented in scipy.stats.
I am building a classifier for some 2D data.
I have some training data for which I know the classes and have plotted these on a graph to see the clustering.
To the observer, there are obvious, separate clusters, but unfortunately they are spread out over lines rather than in tight clusters. One line-spread goes up at about an 80 degree angle, another at 45 degree and another at about 10 degrees from horizontal, but all three seem to point back to the origin.
I want to perform a nearest-neighbour classification on some test data, and from the looks of things, if the test data is very similar to the training data a 3-nearest-neighbour classifier would work fine, except when the data is close to the origin of the graph, in which case the three clusters are quite close together and there might be a few errors.
Should I be coming up with some estimated gaussian distributions for my clusters? If so, I'm not sure how I can combine this with a nearest neighbour classifier?
Be grateful for any input.
Cheers
Transform all your points to [r, angle], and scale r down to the range 0 to 90 too, before running nearest-neighbor.
Why ? NN uses Euclidean distance between points and centres (in most implementations),
but you want distance( point, centre ) to be more like
sqrt( (point.r - centre.r)^2 + (point.angle - centre.angle)^2 )
than sqrt( (point.x - centre.x)^2 + (point.y - centre.y)^2 ) .
Scaling r down to 30 ? 10 ? would weight angle more than r, which seems to be what you want.
Why use k-NN for that purpose? any linear classifier would do the trick. try solving it with SVM and you'll get much better results.
If you insist of using kNN, you clearly have to scale the features and transform them into polar ones as mentioned here.
Hey i am trying to calculate a cosinor analysis in statistica but am at a loss as to how to do so. I need to calculate the MESOR, AMPLITUDE, and ACROPHASE of ciracadian rhythm data.
http://www.wepapers.com/Papers/73565/Cosinor_analysis_of_accident_risk_using__SPSS%27s_regression_procedures.ppt
there is a link that shows how to do it, the formulas and such, but it has not given me much help. Does anyone know the code for it, either in statistica or SPSS??
I really need to get this done because it is for an important paper
I don't have SPSS or Statistica, so I can't tell you the exact "push-this-button" kind of steps, but perhaps this will help.
Cosinor analysis is fitting a cosine (or sine) curve with a known period. The main idea is that the non-linear problem of fitting a cosine function can be reduced to a problem that is linear in its parameters if the period is known. I will assume that your period T=24 hours.
You should already have two variables: Time at which the measurement is taken, and Value of the measurement (these, of course, might be called something else).
Now create two new variables: SinTime = sin(2 x pi x Time / 24) and CosTime = cos(2 x pi x Time / 24) - this is desribed on p.11 of the presentation you linked (x is multiplication). Use pi=3.1415 if the exact value is not built-in.
Run multiple linear regression with Value as outcome and SinTime and CosTime as two predictors. You should get estimates of their coefficients, which we will call A and B.
The intercept term of the regression model is the MESOR.
The AMPLITUDE is sqrt(A^2 + B^2) [square root of A squared plus B squared]
The ACROPHASE is arctan(- B / A), where arctan is the inverse function of tan. The last two formulas are from p.14 of the presentation.
The regression model should also give you an R-squared value to see how well the 24 hour circadian pattern fits the data, and an overall p-value that tests for the presence of a circadian component with period 24 hrs.
One can get standard errors on amplitude and phase using standard error propogation formulas, but that is not included in the presentation.