I have trouble intrepreting the result which I get from the segregation.test method in spatstat. However, I have three different point patterns A,B,C and I want to prove that C and B are correlating whereas A and B not. You can see the Kernel estimates of intensity in this picture:
But computing this in R with spatstat package I always get the same p-value, although the test statistic T is different… How is this possible? What does the test statistic T mean in this context? And why do I get the exact same p-value?
I hope you can help what I did wrong doing this Monte Carlo test.
The meaning of the test statistic T is clearly explained in the help file. Did you look at it?
?segregation.test
Under the null hypothesis of no segregation in the Monte Carlo test the data pattern and the simulated patterns are exchangeable. The p-value is calculated by the rank of the test statistic of the observed pattern out of the total number of patterns. In both cases you have presented the observed data had the most extreme segregation statistic T, and the p-value is 1/26 = 0.03846.
To understand the details look at the mentioned help file and Chapters 10 and 14 of the spatstat book. (Unfortunately none of these are free sample chapters.)
Edit: The test statistic T is a measure of the degree of segregation. If the points are randomly labeled it tends to be close to 0 and if the marks are very well separated it tends to be numerically "large". Since there is no notion of "large" the Monte Carlo p-value is used to judge whether the observed T is so large that we should reject the null hypothesis of random labeling.
Related
I know when random forest (RF) is used for classification, the AUC normally is used to assess the quality of classification after applying it to test data. However,I have no clue the parameter to assess the quality of regression with RF. Now I want to use RF for the regression analysis, e.g. using a metrics with several hundreds samples and features to predict the concentration (numerical) of chemicals.
The first step is to run randomForest to build the regression model, with y as continuous numerics. How can I know whether the model is good or not, based on the Mean of squared residuals and % Var explained? Sometime my % Var explained is negative.
Afterwards, if the model is fine and/or used straightforward for test data, and I get the predicted values. Now how can I assess the predicted values good or not? I read online some calculated the accuracy (formula: 1-abs(predicted-actual)/actual), which also makes sense to me. However, I have many zero values in my actual dataset, are there any other solutions to assess the accuracy of predicted values?
Looking forward to any suggestions and thanks in advance.
The randomForest R package comes with an importance function which can used to determine the accuracy of a model. From the documentation:
importance(x, type=NULL, class=NULL, scale=TRUE, ...), where x is the output from your initial call to randomForest.
There are two types of importance measurements. One uses a permutation of out of bag data to test the accuracy of the model. The other uses the GINI index. Again, from the documentation:
Here are the definitions of the variable importance measures. The first measure is computed from permuting OOB data: For each tree, the prediction error on the out-of-bag portion of the data is recorded (error rate for classification, MSE for regression). Then the same is done after permuting each predictor variable. The difference between the two are then averaged over all trees, and normalized by the standard deviation of the differences. If the standard deviation of the differences is equal to 0 for a variable, the division is not done (but the average is almost always equal to 0 in that case).
The second measure is the total decrease in node impurities from splitting on the variable, averaged over all trees. For classification, the node impurity is measured by the Gini index. For regression, it is measured by residual sum of squares.
For further information, one more simple importance check you may do, really more of a sanity check than anything else, is to use something called the best constant model. The best constant model has a constant output, which is the mean of all responses in the test data set. The best constant model can be assumed to be the crudest model possible. You may compare the average performance of your random forest model against the best constant model, for a given set of test data. If the latter does not outperform the former by at least a factor of say 3-5, then your RF model is not very good.
I'm working on a classification problem (predicting three classes) and I'm comparing SVM against Random Forest in R.
For evaluation and comparison I want to calculate the bias and variance of the models. I've looked up the two terms in many machine learning books and I'd say I do understand the sense of variance and bias (easiest explanation with the bullseye). But I can't really figure out how to apply it in my case.
Let's say I predict the results for a test set with 4 SVM-models that were trained with 4 different training sets. Each time I get a total error (meaning all wrong predictions/all predictions).
Do I then get the bias for SVM by calculating this?
which would mean that the bias is more or less the mean of the errors?
I hope you can help me with not to complicated formula, because I've already seen many of them.
First post!
I'm a biologist with limited background in applied statistics and R. Basically know enough to be dangerous, so I'd appreciate it someone could confirm/deny that I'm on the right path.
My datasets consists of count data (wildlife visits to water wells) as a response variable and multiple continuous predictor variables (environmental measurements).
First, I eliminated multicolinearity by dropping a few predictor variables. Second, I investigated the distribution of the response variable. Initially, it looked Poisson. However, a Poisson exact test came back as significant, and the variance of the response variable was around 200 with a mean around 9, i.e. overdispersed. Due to this, I decided to move forward with Negative Binomial and Quasipoisson regressions. Both selected the same model, the residuals of which are in a normal distribution. Further, a plot of residuals over predicted values is unbiased and homoscedastic.
Questions:
1. Have I selected the correct regressions to model this data?
2. Are there additional assumptions of the NBR and QpR that I need to test? How should I/Where can I learn about how to do these?
3. Did I check for overdispersion correctly? Is there a difference in comparing the mean and variance vs comparing the conditional mean and variance of the response variable?
4. While the NBR and QpR called the same model, is there a way to select which is the "better" approach?
5. I would like to eventually publish. Are there more analyses I should perform on my selected model?
I want to know the goodness of fit while fitting a power law distribution in R using poweRlaw package.
After estimate_xmin() , I had a p-value 0.04614726. But the bootstrap_p() returns another p-value 0.
So why do these two p-value differ? And how can I judge if it is a power law distribution?
here is the plot when using poweRlaw for fittingpoweRlaw fitting result
You're getting a bit confused. One of the statistics that estimate_xmin returns is the Kolmogorov-Smirnoff statistic (as described in Clauset, Shalizi, Newman (2009)). This statistic is used to estimate the best cut-off value for your model, i.e. xmin. However, this doesn't tell you anything about the model fit.
To assess model suitability is where the bootstrap function comes in.
I want to fit a distribution to my data. I use fitdistrplus package in r to find the distribution. I can compare the goodness of fit results for different distributions to see which one is more fitted to my data but I don't know how to check the pvalue for goodness of fit test for each of the distributions. The results might show that among gamma, lognormal and exponential, exponential distribution has the lower statistics for anderson darling test but I don't know how to check if pvalue for these tests does not reject the null hypothesis. Is there any built in function in R which gives the pvalues?
Here is a piece of code I used as an example:
d <- sample(100,50)
library(fitdistrplus)
descdist(d)
fitg <- fitdist(d,"gamma")
fitg2 <- fitdist(d,"exp")
gofstat(list(fitg,fitg2))
This code makes 50 random numbers from 0 to 100 and tries to find best fitted model to these data. If descdist(d) shows that gamma and exponential are the two candidates as the best fitted model, fitg and fitg2 finds their related models. the last line compares Ks and anderson darling statistics to show which distribution is most fitted. Distribution with lower value for these tests is the best. However, I dont know how to find p-values for fitg and fitg2 before comparying them. If pvalues show that none of these distributions are not fitted to these data, there is no point to comparing their goodness of fit statistics to my knowledge.
Any help is appreciated.
Thanks