I have two groups in which I compare two times (before and after treatment).
At first, I tried an repeated measures ANOVA and observed significant difference between groups. However, I have the following question: baseline means (time 1) are very different between groups and we fear that the significant result of ANOVA is due to this difference between baselines.
Therefore, we consider using another statistical model, specifically mixed models. However, the SPSS does not run telling me that "no valid case was found".
I talked to a statistician who said the problem is that the number of observations (rows) is less than the number of columns (dependent variables).
Would anyone know if this information makes sense? And does anyone know of any statistical model that would help us control this difference between baselines using SPSS?
Related
I'm currently evaluating a recommender system based on implicit feedback. I've been a bit confused with regard to the evaluation metrics for ranking tasks. Specifically, I am looking to evaluate by both precision and recall.
Precision#k has the advantage of not requiring any estimate of the
size of the set of relevant documents but the disadvantages that it is
the least stable of the commonly used evaluation measures and that it
does not average well, since the total number of relevant documents
for a query has a strong influence on precision at k
I have noticed myself that it tends to be quite volatile and as such, I would like to average the results from multiple evaluation logs.
I was wondering; say if I run an evaluation function which returns the following array:
Numpy array containing precision#k scores for each user.
And now I have an array for all of the precision#3 scores across my dataset.
If I take the mean of this array and average across say, 20 different scores: Is this equivalent to Mean Average Precision#K or MAP#K or am I understanding this a little too literally?
I am writing a dissertation with an evaluation section so the accuracy of the definitions is quite important to me.
There are two averages involved which make the concepts somehow obscure, but they are pretty straightforward -at least in the recsys context-, let me clarify them:
P#K
How many relevant items are present in the top-k recommendations of your system
For example, to calculate P#3: take the top 3 recommendations for a given user and check how many of them are good ones. That number divided by 3 gives you the P#3
AP#K
The mean of P#i for i=1, ..., K.
For example, to calculate AP#3: sum P#1, P#2 and P#3 and divide that value by 3
AP#K is typically calculated for one user.
MAP#K
The mean of the AP#K for all the users.
For example, to calculate MAP#3: sum AP#3 for all the users and divide that value by the amount of users
If you are a programmer, you can check this code, which is the implementation of the functions apk and mapk of ml_metrics, a library mantained by the CTO of Kaggle.
Hope it helped!
I'm Trying to use machine learning in my job, but I can't find a way to adapt it to what I need. And I don't know if it is already a known problem or if I'm working with something that doesn't have a known solution yet.
Let's say that I have a lot of independent variables, encoded as onehot, and a dependent variable with only two status: True (The result had an error) and False (The result was successful)
My independent variables are the parameters I use for a query in an API, and the result is the one that returned the API.
My objective is to detect a pattern where I can see in a dataset in a certain timeframe of a few hours, the failing parameters, so I can avoid to query the API if I'm certain that it could fail.
(I'm working with millions of queries per day, and this mechanism is critical for a good user experience)
I'll try to make an example so you can understand what I need.
Suppose that I have a delivery company, I count with 3 trucks, and 3 different routes I could take.
So, my dummy variables would be T1,T2,T3,R1,R2 and R3 (I could delete T3 and R3 since there are considered by the omission of the other 2)
Then, I have a big dataset of the times that the delivery was delayed. So: Delayed=1 or Delayed=0
With this, I would have a set like this:
T1_|_T2_|_T3_|_R1_|_R2_|_R3||Delayed
------------------------------------
_1_|_0__|_0__|_1__|_0__|_0_||____0__
_1_|_0__|_0__|_0__|_1__|_0_||____1__
_0_|_1__|_0__|_1__|_0__|_0_||____0__
_1_|_0__|_0__|_0__|_1__|_0_||____1__
_1_|_0__|_0__|_1__|_0__|_0_||____0__
Not only I want to say "in most cases, truck 1 arrives late, it could have a problem, I shouldn't send it more", that is a valid result too, but I also want to detect things like: "in most cases, truck 1 arrives late when it goes in the route 1, probably this type of truck has a problem on this specific route"
This dataset is an example, the real one is huge, with thousand of dependent variables, so it could probably have more than one problem in the same dataset.
example: truck 1 has problems in route 1, and truck 3 has problems in route 1.
example2: truck 1 has problems in route 1, and truck 3 has problems in any route.
So, I would make a blacklist like:
example: Block if (truck=1 AND route=1) OR (truck=3 AND route=1)
example2: Block if (truck=1 AND route=1) OR truck=3
I'm actually doing this without machine learning, with an ugly code that makes a massive cartesian product of the independent columns, and counts the quantity of "delayed". Then I choose the worst delayed/total proportion, I blacklist it, and I iterate again with new values.
This errors are commonly temporary, so I would send a new dataset every few hours, I don't need a lifetime span analysis, except that the algorithm considers these temporary issues.
Anyone has a clue of what can I use, or where can I investigate about it?
Don't hesitate to ask for more info if you need it.
Thanks in advance!
Regards
You should check out the scikit-learn package for machine learning classifiers (Random Forest is an industry standard). For this problem, you could feed a portion of the data (training set, say 80% of the data) to the model and it would learn how to predict the outcome variable (delayed/not delayed).
You can then test the accuracy of your model by 'testing' on the remaining 20% of your data (the test set), to see if your model is any good at predicting the correct outcome. This will give you a % accuracy. Higher is better generally, unless you have severely imbalanced classes, in which case your classifier will just always predict the more common class for easy high accuracy.
Finally, if the accuracy is satisfactory, you can find out which predictor variables your model considered most important to achieve that level of prediction, i.e. Variable Importance. I think this is what you're after. So running this every few hours would tell you exactly which features (columns) in your set are best at predicting if a truck is late.
Obviously, this is all easier said than done and often you will have to perform significant cleaning of your data, sometimes normalisation (not in the case of random forests though), sometimes weighting your classifications, sometimes engineering new features... there is a reason this is a dedicated profession.
Essentially what you're asking is "how do I do Data Science?". Hopefully this will get you started, the rest (i.e. learning) is on you.
I have implemented a recommender system based upon matrix factorization techniques. I want to evaluate it.
I want to use 10-fold-cross validation with All-but-one protocol (https://ai2-s2-pdfs.s3.amazonaws.com/0fcc/45600283abca12ea2f422e3fb2575f4c7fc0.pdf).
My data set has the following structure:
user_id,item_id,rating
1,1,2
1,2,5
1,3,0
2,1,5
...
It's confusing for me to think how the data is going to be splitted, because I can't put some triples (user,item,rating) in the testing set. For example, if I select the triple (2,1,5) to the testing set and this is the only rating user 2 has made, there won't be any other information about this user and the trained model won't predict any values for him.
Considering this scenario, how should I do the splitting?
You didn't specify a language or toolset so I cannot give you a concise answer that is 100% applicable to you, but here's the approach I took to solve this same exact problem.
I'm working on a recommender system using Treasure Data (i.e. Presto) and implicit observations, and ran into a problem with my matrix where some users and items were not present. I had to re-write the algorithm to split the observations into train and test so that every user and every item would be represented in the training data. For the description of my algorithm I assume there are more users than items. If this is not true for you then just swap the two. Here's my algorithm.
Select one observation for each user
For each item that has only one observation and has not already been selected from the previous step select one observation
Merge the results of the previous two steps together.
This should produce a set of observations that covers all of the users and all of the items.
Calculate how many observations you need to fill your training set (generally 80% of the total number of observations)
Calculate how many observations are in the merged set from step 3.
The difference between steps 4 and 5 is the number of remaining observations necessary to fill the training set.
Randomly select enough of the remaining observations to fill the training set.
Merge the sets from step 3 and 6: this is your training set.
The remaining observations is your testing set.
As I mentioned, I'm doing this using Treasure Data and Presto so the only tool I have at my disposal is SQL, common table expressions, temporary tables, and Treasure Data workflow.
You're quite correct in your basic logic: if you have only one observation in a class, you must include that in the training set for the model to have any validity in that class.
However, dividing the input into these classes depends on the interactions among various observations. Can you identify classes of data, such as the "only rating" issue you mentioned? As you find other small classes, you'll also need to ensure that you have enough of those observations in your training data.
Unfortunately, this is a process that's tricky to automate. Most one-time applications simply have to hand-pick those observations from the data, and then distribute the others per normal divisions. This does have a problem that the special cases are over-represented in the training set, which can detract somewhat from the normal cases in training the model.
Do you have the capability of tuning the model as you encounter later data? This is generally the best way to handle sparse classes of input.
collaborative filtering (matrix factorization) can't have a good recommendation for an unseen user with no feedback. Nevertheless, an evaluation should consider this case and take it into account.
One thing you can do is to report performance for all test users, just test users with some feedback and just unseen users with no feedback.
So I'd say keep the test, train split random but evaluate separately for unseen users.
More info here.
Im new to &investigating Machine Learning. I have a use case & data but I am unsure of a few things, mainly how my model will run, and what model to start with. Details of the use case and questions are below. Any advice is appreciated.
My Main question is:
When basing a result on scores that are accumulated over time, is it possible to design a model to run on a continuous basis so it gives a best guess at all times, be it run on day one or 3 months into the semester?
What model should I start with? I was thinking a classifier, but ranking might be interesting also.
Use Case Details
Apprentices take a semesterized course, 4 semesters long, each 6 months in duration. Over the course of a semester, apprentices perform various operations and processes & are scored on how well they do. After each semester, the apprentices either have sufficient score to move on to semester 2, or they fail.
We are investigating building a model that will help identify apprentices who are in danger of failing, with enough time for them to receive help.
Each procedure is assigned a complexity code of simple, intermediate or advanced, and are weighted by complexity.
Regarding Features, we have the following: -
Initial interview scores
Entry Exam Scores
Total number of simple procedures each apprentice performed
Total number of intermediate procedures each apprentice performed
Total number of advanced procedures each apprentice performed
Average score for each complexity level
Demograph information (nationality, age, gender)
I am unsure of is how the model will work and when we will run it. i.e. - if we run it on day one of the semester, I assume everyone will fail as everyone has procedure scores of 0
Current plan is to run the model 2-3 months into each semester, so there is enough score data & also enough time to help any apprentices who are in danger of failing.
This definitely looks like a classification model problem:
y = f(x[0],x[1], ..., x[N-1])
where y (boolean output) = {pass, fail} and x[i] are different features.
There is a plethora of ML classification models like Naive Bayes, Neural Networks, Decision Trees, etc. which can be used depending upon the type of the data. In case you are looking for an answer which suggests a particular ML model, then I would need more data for the same. However, in general, this flow-chart can be helpful in selection of the same. You can also read about Model Selection from Andrew-Ng's CS229's 5th lecture.
Now coming back to the basic methodology, some of these features like initial interview scores, entry exam scores, etc. you already know in advance. Whereas, some of them like performance in procedures are known over the semester.
So, there is no harm in saying that the model will always predict better towards the end of each semester.
However, I can make a few suggestions to make it even better:
Instead of taking the initial procedure-scores as 0, take them as a mean/median of the past performances in other procedures by the subject-apprentice.
You can even build a sub-model to analyze the relation between procedure-scores and interview-scores as they are not completely independent. (I will explain this sentence in the later part of the answer)
However, if the semester is very first semester of the subject-apprentice, then you won't have such data already present for that apprentice. In that case, you might need to consider the average performances of other apprentices with similar profiles as the subject-apprentice. If the data-set is not very large, K Nearest Neighbors approach can be quite useful here. However, for large data-sets, KNN suffers from the curse of dimensionality.
Also, plot a graph between y and different variables x[i], so as to see the independent variation of y with respect to each variable.
Most probably (although it's just a hypotheses), y will depend more the initial variables in comparison the variables achieved later. The reason being that the later variables are not completely independent of the former variables.
My point is, if a model can be created to predict the output of a semester, then, a similar model can be created to predict just the output of the 1st procedure-test.
In the end, as the model might be heavily based on demographic factors and other things, it might not be a very successful model. For the same reason, we cannot accurately predict election results, soccer match results, etc. As they are heavily dependent upon real-time dynamic data.
For dynamic predictions based on different procedure performances, Time Series Analysis can be a bit helpful. But in any case, the final result will heavily dependent on the apprentice's continuity in motivation and performance which will become more clear towards the end of each semester.
i am fairly new with statitistic.
I made an experiment and used the two way ANOVA with repeated measures. The calculation was done in SPSS. In most papers I have seen, the f-value and the degree of freedom were reported as well. is it normal to report those values as well? if so, which values do i take from the spss output.
how do I interpret these values? what do they mean?
when does the f-value support a significant result and when not?
what are good values for the f-value and the degree of freedom.
in some article is also read about the critical f-values, how do I get this value?
most articles describe how to calculate those values but do not explain their meaning for the experiment.
some clarification in these issues is greatly appreciated.
My English is not very good, but I will try to answer your question.
The main purpose of ANOVA is that we want statistical proof that the measured groups have the same mean or not. So we make a null hypothesis and an alternative hypothesis, then we use a test statistics on the data. You can use ANOVA if the groups has the same variance (squared standard deviation).
You need to test this. This is a hyptest too, the nullhyp. is the groups have the same variance, the anternative hyp. is they dont.
You need to make decision from the Sig. value, if the value is higher than 0,05, we usually accept the nullhyp. If the variances are equal, we can use ANOVA. (I assume that the data is following the Normal distribution.) The nullhyp. is that the groups have equal means, the alternative hyp is that we have at least 1 group with a different mean. You can make your decision from the Sig. value, as I said before, if the value higher than 0.05 we accept the nullhyp. The F-critical value is not important if you are calculating on a computer. You can make an accepting interval from the lower and the upper F-critical, and if the F-value is in the interval you accept the nullhyp, but I only used this method in statistics class. You don't need the F-value and the df in the report, because they don't explain anything on their own.