When conducting Latent Class Analysis sometimes the information criterion (i.e., AIC, BIC, aBIC) don't select the same model. Such is the case in a study of substance use patterns that I am conducting among 774 men who have sex with men. Figure 1 shows the fit criterion plotted for each number of latent classes. BIC and CAIC select the three class model (See Figure 2). However, the aBIC selects a five class model (See Figure 2).
How do you select a model solution under these circumstances? Is there a way to select variables or collapse variables down in order to optimize results?
It is never easy to select the number of classes for LCA, but there are some rules of thumb that I follow:
Based on Nylund, Asparouhov & Muthén (2007) you want to follow BIC and bootstrap likelihood ratio test (BLRT). Even then, they seldom agree – BLRT will tell you to pick a model with more classes, BIC will be more conservative and suggest fewer classes. But this is as close as you can get by using statistical tests.
Rely on the available theory underlying your model. Look for potential discrepancies with your theoretical knowledge and try to deduce from the theory how many classes are to be expected. There is no golden rule, LCA is a good method, but without theory it is quite meaningless. If you have little theory, what you can do to double check your findings is to relate your latent variable to a distal outcome (covariate) about which you might have some theory and see if it works out. For example, you suspect that one of your latent classes will be dominated by one gender: associate your latent variable with gender and see.
Parsimony rule: simple models are preferred to complex ones (Collins & Lanza, 2010). If a simpler model does all the work, why choose a complex one?
In your case, I would start with a 3 class model, since it is suggested by BIC and parsimony. After finishing the analysis and interpreting the findings, I would re-run the model with 4/5 classes and see if I would reach substantially different findings - something that is worth reporting on, any important or contradicting findings to what I have found with a 3 class model. If it just adds complexity, but does not contradict or improve what I have already known, I'd stick to a 3 class model.
Looking at the results, I think that the 5 class model does not provide anything beyond the 3 classes. In the 3 class model, you have one class of extensive drug users (16%), moderate drug users dominated by cannabis, popper, hallucinogens and cocaine (40%), and finally a class of light users dominated by alcohol and cannabis (44%). The 5 class model split the first two groups into specific smaller sub-groups, but you have to decide whether these splits are important for your research - whether they make sense for your research question.
I would also recommend checking bivariate residuals. It is possible that the model misfit that is suggesting more classes is generated by a residual association between your indicators. If you can justify it theoretically (for example by finding some similarity between the indicators beyond the latent class), you can add the residual association and obtain a similarly good fit with the 3 class model.
One last point, avoid using AIC for LCA altogether - it is a very poorly performing index! Use cAIC, BIC and aBIC instead. AIC does not correct for the sample size, which can be quite problematic with larger samples.
Sources:
Collins, L. M., & Lanza, S. T. (2010). Latent class and latent transition analysis: With applications in the social, behavioral, and health sciences. New York: Wiley.
Related
I have developed a pipeline to extract text from documents, preprocess the text, and train a gensim Doc2vec model on given documents. Given a document in my corpus, I would like to recommend other documents in the corpus.
I want to know how I can evaluate my model without having a pre-defined list of "good" recommendations. Any ideas?
One simple self-check that can be used to catch some big problems with a Doc2Vec model training pipeline – like gross misparameterizations, or insufficient data/epochs – is to re-infer vectors for the training texts (using .infer_vector()), and check that generally:
the bulk-trained vector for the same text is "close to" the re-inferred vector - such as its nearest-neighbor, or one of the top neighbors, in a .most_similar() operation on the re-inferred text
the overall list of nearest-neighbors (from .most_similar()) for the bulk-trained vector, & the re-inferred vector, are very similar.
They won't necessarily be identical, for reasons explained in Q11 & Q12 of the Gensim Project FAQ, but if they're wildly-different, then something foundational has gone wrong, like:
insufficient (in quantity or quality/form) training data
misparameterizations, like too few epochs or too-large (overfitting-prone) vectors for the quantity of data
Ultimately, though, the variety of data sources & intended uses & possible dimensions of "recommendation-worthy" mean that you need cusomt inputs, based on your project's needs, usually from the intended audience (or your own ability to simulate/represent it).
In the original paper introducing the "Paragraph Vector" algorithm (what's inside the Doc2Vec class), and a followup evaluating it on Wikipedia & arXiv articles, several of the evaluations used triplets of documents, where 2 of the triplet were conjectured to be "necessarily similar" based on some preexisting system's groupings, and the 3rd randomly-chosen.
The algorithm's performance, and relative performance under different parameter choices, was scored based on how often it placed the 2 presumptively-related documents closer-together than the 3rd randomly-chosen document.
For example, one of the original paper's evaluations use brief search-engine-result snippets as documents, and considered any 2 documents that appeared as sibling top-10 results for the same query as presumptively-related. Two of the followup paper's evaluation used the human-curated categories of Wikipedia or arXiv as signalling that articles of the same category should be presumptively-related.
It's imperfect, but allowed the creation of large evaluation sets from already-existing systems/data, which generally pointed results in the same direction as human senses-of-relatedness.
Perhaps you can find a similar preexisting guide for your data. Or, as you perform ad-hoc checking, be sure to capture every judgement you make, so that it becomes, over time, a growing dataset of desirable pairings that are either (a) better than some other result that was co-presented; or (b) just "presumably good enough" that they usually should rank higher than other random 3rd documents. A large amount of imprecision in such desirability-data is tolerable, as it can even out as the set of probe-pairings grows, and the power of being able to automate bulk quantitative evaluations (reusing old assessments against new parameters/models) drives far more overall improvement than any small glitches in the evaluations cost.
Basically I'm modelling tree fruiting patterns using mgcv bams and auto regressive (1) models have much better outcomes using itsadug::compareML(). (bam AR(1) was chosen due to limitations associated with binomial data) Further, this AR is backed up by biological theory. However, the best models when I use AR techniques often don't include terms that are included in the non-AR models. I understand this to be a common occurrence, the AR term explains much of the variance, leaving smaller predictions for the remaining terms.
I've seen discussions on here warning that AR GAMs should be interpreted with care, and Gavin Simposon's AR GAM post (part 1), ends with hinting that there are some serious diagnostic criteria that should be considered, but part 2 never came out, and I'm struggling to find resources on interpretation. Much more common are simple introductory articles.
I guess the fundamental question is thus: the two different types of model will make different statements about the effects of a given predictor, which should be believed?
If the non-AR model finds that month is a useful predictor, but the AR model finds it ultimately superfluous, does month have an effect? Is month relevant due to effects like light patterns, or just because of correlational structure? I guess this is a classic 'no models are true, some are useful' situation.
This problem persists even inside of a predictor. My temperature:vpds tensor product spline will cite a particular region as increasing the probability in non-AR models, but will suggest another region does so in AR models (in addition to the first).
I'm presently leaning towards including both sets of models in my paper, and noting that the AR models provide better predictions, but the non-AR models can provide insight into the effect of variables. Even then I wonder what's more useful? The model that best fits the data without any AR? Or the non-AR version of the AR model (i.e, set the autocorrelation parameter to 0 keeping the same predictors). I'm leaning towards the former, because I feel strange about the models that have almost no predictors.
I am trying to predict test reuslts based on known previous scores. The test is made up of three subjects, each contributing to the final exam score. For all students I have their previous scores for mini-tests in each of the three subjects, and I know which teacher they had. For half of the students (the training set) I have their final score, for the other half I don't (the test set). I want predict their final score.
So the test set looks like this:
student teacher subject1score subject2score subject3score finalscore
while the test set is the same but without the final score
student teacher subject1score subject2score subject3score
So I want to predict the final score of the test set students. Any ideas for a simple learning algorithm or statistical technique to use?
The simplest and most reasonable method to try is a linear regression, with the teacher and the three scores used as predictors. (This is based on the assumption that the teacher and the three test scores will each have some predictive ability towards the final exam, but they could contribute differently- for example, the third test might matter the most).
You don't mention a specific language, but let's say you loaded it into R as two data frames called 'training.scoresandtest.scores`. Fitting the model would be as simple as using lm:
lm.fit = lm(finalscore ~ teacher + subject1score + subject2score + subject3score, training.scores)
And then the prediction would be done as:
predicted.scores = predict(lm.fit, test.scores)
Googling for "R linear regression", "R linear models", or similar searches will find many resources that can help. You can also learn about slightly more sophisticated methods such as generalized linear models or generalized additive models, which are almost as easy to perform as the above.
ETA: There have been books written about the topic of interpreting linear regression- an example simple guide is here. In general, you'll be printing summary(lm.fit) to print a bunch of information about the fit. You'll see a table of coefficients in the output that will look something like:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -14.4511 7.0938 -2.037 0.057516 .
setting 0.2706 0.1079 2.507 0.022629 *
effort 0.9677 0.2250 4.301 0.000484 ***
The Estimate will give you an idea how strong the effect of that variable was, while the p-values (Pr(>|T|)) give you an idea whether each variable actually helped or was due to random noise. There's a lot more to it, but I invite you to read the excellent resources available online.
Also plot(lm.fit) will graphs of the residuals (residuals mean the amount each prediction is off by in your testing set), which tells you can use to determine whether the assumptions of the model are fair.
I'm doing some semantic-web/nlp research, and I have a set of sparse records, containing a mix of numeric and non-numeric data, representing entities labeled with various features extracted from simple English sentences.
e.g.
uid|features
87w39423|speaker=432, session=43242, sentence=34, obj_called=bob,favorite_color_is=blue
4535k3l535|speaker=512, session=2384, sentence=7, obj_called=tree,isa=plant,located_on=wilson_street
23432424|speaker=997, session=8945305, sentence=32, obj_called=salty,isa=cat,eats=mice
09834502|speaker=876, session=43242, sentence=56, obj_called=the monkey,ate=the banana
928374923|speaker=876, session=43242, sentence=57, obj_called=it,was=delicious
294234234|speaker=876, session=43243, sentence=58, obj_called=the monkey,ate=the banana
sd09f8098|speaker=876, session=43243, sentence=59, obj_called=it,was=hungry
...
A single entity may appear more than once (but with a different UID each time), and may have overlapping features with its other occurrences. A second data set represents which of the above UIDs are definitely the same.
e.g.
uid|sameas
87w39423|234k2j,234l24jlsd,dsdf9887s
4535k3l535|09d8fgdg0d9,l2jk34kl,sd9f08sf
23432424|io43po5,2l3jk42,sdf90s8df
09834502|294234234,sd09f8098
...
What algorithm(s) would I use to incrementally train a classifier that could take a set of features, and instantly recommend the N most similar UIDs and probability of whether or not those UIDs actually represent the same entity? Optionally, I'd also like to get a recommendation of missing features to populate and then re-classify to get a more certain matches.
I researched traditional approximate nearest neighbor algorithms. such as FLANN and ANN, and I don't think these would be appropriate since they're not trainable (in a supervised learning sense) nor are they typically designed for sparse non-numeric input.
As a very naive first-attempt, I was thinking about using a naive bayesian classifier, by converting each SameAs relation into a set of training samples. So, for each entity A with B sameas relations, I would iterate over each and train the classifier like:
classifier = Classifier()
for entity,sameas_entities in sameas_dataset:
entity_features = get_features(entity)
for other_entity in sameas_entities:
other_entity_features = get_features(other_entity)
classifier.train(cls=entity, ['left_'+f for f in entity_features] + ['right_'+f for f in other_entity_features])
classifier.train(cls=other_entity, ['left_'+f for f in other_entity_features] + ['right_'+f for f in entity_features])
And then use it like:
>>> print classifier.findSameAs(dict(speaker=997, session=8945305, sentence=32, obj_called='salty',isa='cat',eats='mice'), n=7)
[(1.0, '23432424'),(0.999, 'io43po5', (1.0, '2l3jk42'), (1.0, 'sdf90s8df'), (0.76, 'jerwljk'), (0.34, 'rlekwj32424'), (0.08, '09843jlk')]
>>> print classifier.findSameAs(dict(isa='cat',eats='mice'), n=7)
[(0.09, '23432424'), (0.06, 'jerwljk'), (0.03, 'rlekwj32424'), (0.001, '09843jlk')]
>>> print classifier.findMissingFeatures(dict(isa='cat',eats='mice'), n=4)
['obj_called','has_fur','has_claws','lives_at_zoo']
How viable is this approach? The initial batch training would be horribly slow, at least O(N^2), but incremental training support would allow updates to happen more quickly.
What are better approaches?
I think this is more of a clustering than a classification problem. Your entities are data points and the sameas data is a mapping of entities to clusters. In this case, clusters are the distinct 'things' your entities refer to.
You might want to take a look at semi-supervised clustering. A brief google search turned up the paper Active Semi-Supervision for Pairwise Constrained Clustering which gives pseudocode for an algorithm that is incremental/active and uses supervision in the sense that it takes training data indicating which entities are or are not in the same cluster. You could derive this easily from your sameas data, assuming that - for example - uids 87w39423 and 4535k3l535 are definitely distinct things.
However, to get this to work you need to come up with a distance metric based on the features in the data. You have a lot of options here, for example you could use a simple Hamming distance on the features, but the choice of metric function here is a little bit arbitrary. I'm not aware of any good ways of choosing the metric, but perhaps you have already looked into this when you were considering nearest neighbour algorithms.
You can come up with confidence scores using the distance metric from the centres of the clusters. If you want an actual probability of membership then you would want to use a probabilistic clustering model, like a Gaussian mixture model. There's quite a lot of software to do Gaussian mixture modelling, I don't know of any that is semi-supervised or incremental.
There may be other suitable approaches if the question you wanted to answer was something like "given an entity, which other entities are likely to refer to the same thing?", but I don't think that is what you are after.
You may want to take a look at this method:
"Large Scale Online Learning of Image Similarity Through Ranking" Gal Chechik, Varun Sharma, Uri Shalit and Samy Bengio, Journal of Machine Learning Research (2010).
[PDF] [Project homepage]
More thoughts:
What do you mean by 'entity'? Is entity the thing that is referred by 'obj_called'? Do you use the content of 'obj_called' to match different entities, e.g. 'John' is similar to 'John Doe'? Do you use proximity between sentences to indicate similar entities? What is the greater goal (task) of the mapping?
I am hand tagging twitter messages as Positive, Negative, Neutral. I am try to appreciate is there some logic one can use to identify of the training set what proportion of message should be positive / negative and neutral ?
So for e.g. if I am training a Naive Bayes classifier with 1000 twitter messages should the proportion of pos : neg : neutral be 33 % : 33% : 33% or should it be 25 % : 25 % : 50 %
Logically in my head it seems that I i train (i.e. give more samples for neutral) that the system would be better at identifying neutral sentences then whether they are positive or negative - is that true ? or I am missing some theory here ?
Thanks
Rahul
The problem you're referring to is known as the imbalance problem. Many machine learning algorithms perform badly when confronted with imbalanced training data, i.e. when the instances of one class heavily outnumber those of the other class. Read this article to get a good overview of the problem and how to approach it. For techniques like naive bayes or decision trees it is always a good idea to balance your data somehow, e.g. by random oversampling (explained in the references paper). I disagree with mjv's suggestion to have a training set match the proportions in the real world. This may be appropriate in some cases but I'm quite confident it's not in your setting. For a classification problem like the one you describe, the more the sizes of the class sets differ, the more most ML algorithms will have problems discriminating the classes properly. However, you can always use the information about which class is the largest in reality by taking it as a fallback such that when the classifier's confidence for a particular instance is low or this instance couldn't be classified at all, you would assign it the largest class.
One further remark: finding the positivity/negativity/neutrality in Twitter messages seems to me to be a question of degree. As such, it may be viewes as a regression rather than a classification problem, i.e. instead of a three class scheme you perhaps may want calculate a score which tells you how positive/negative the message is.
There are many other factors... but an important one (in determining a suitable ratio and volume of training data) is the expected distribution of each message category (Positive, Neutral, Negative) in the real world. Effectively, a good baseline for the training set (and the control set) is
[qualitatively] as representative as possible of the whole "population"
[quantitatively] big enough that measurements made from such sets is statistically significant.
The effect of the [relative] abundance of a certain category of messages in the training set is hard to determine; it is in any case a lesser factor -or rather one that is highly sensitive to- other factors. Improvements in the accuracy of the classifier, as a whole, or with regards to a particular category, is typically tied more to the specific implementation of the classifier (eg. is it Bayesian, what are the tokens, are noise token eliminated, is proximity a factor, are we using bi-grams etc...) than to purely quantitative characteristics of the training set.
While the above is generally factual but moderately helpful for the selection of the training set's size and composition, there are ways of determining, post facto, when an adequate size and composition of training data has been supplied.
One way to achieve this is to introduce a control set, i.e. one manually labeled but that is not part of the training set and to measure for different test runs with various subsets of the training set, the recall and precision obtained for each category (or some similar accuracy measurements), for this the classification of the control set. When these measurements do not improve or degrade, beyond what's statistically representative, the size and composition of the training [sub-]set is probably the right one (unless it is an over-fitting set :-(, but that's another issue altogether... )
This approach, implies that one uses a training set that could be 3 to 5 times the size of the training subset effectively needed, so that one can build, randomly (within each category), many different subsets for the various tests.