Most psychometric investigations do not address the problem of generalization outside the sample used to develop the model. Clearly, avoiding cross validation yields inflates results, which are over optimistic and may not replicate when the model is applied to out-of-sample data. Similar results have been recently reported by Bokhari and Hubert Also Pace et al.
The example below Table 1 regards the psychometric identification of malingering Sartori et al. The dataset analyzed here consists in the raw scores on the personality questionnaire MCMI-III that was used to predict whether the test was collected in one of two settings.
Both groups are low credibility groups, the first are fake good suspects they have advantages from denying psychopathology while the second are fake bad suspects they have advantages from doctoring a get-out-of-jail psychopathology. As seen above, if a model is developed on all the available data then the final accuracy will be an over optimistic estimate that is not confirmed when the model is tested on previously unseen data out-of-sample dataset.
Exact replication on the test set show that the 10 fold cross validation does not lead to an overly optimistic estimate. In short, models developed with cross validation replicate well see also Koul et al. Very simple classifiers in terms of parameters that require estimation give comparable results to more complex models compare Naive Bayes and Knn versus Random Forest and Multilayer Neural Network.
Cross validation is therefore approximating results in exact replication with high accuracy. Note that decision rules e. As regards to exact replicability, it has been noted that results, analyzed with statistical inferences techniques, when replicated show a reduced effect size. High performance neural networks are trained with extremely large dataset. It has been well-established that for a given problem, with large enough data, very different algorithms perform virtually the same.
However, in the analysis of psychological experiments typical number of data points is in the range. Do ML classifiers trained on such small dataset maintain their performance?
In order to evaluate the capacity of ML models to replicate classification accuracies on small datasets, we ran a simulation using the dataset used for the simulations reported in Table 1. A total of participants assessed in a low credibility setting in the fake good group and in the fake bad group were administered the MCMI-III as a part of a forensic assessment. The whole dataset was split into four stratified subsets folds.
Each ML model was trained on one of these folds using fold cross validation and tested on the remaining three. The results are reported in Table 2. Table 2. Different machine learning models trained using fold cross validation. As shown in Table 2 all the classifiers trained on a small dataset of 62 cases 32 per each of the two categories perform well on each of the other test folds.
Simple classifiers e. A good strategy in developing ML models that replicates well is to train simple classifiers or ensemble of classifiers rather than models with many parameters. In all the examples reported above the number of cases for each class was equal. Unbalanced datasets are usually a problem for classifiers and usually performance of classifiers is generally poor on the minority class.
For this reason a number of techniques have been developed in order to deal with unbalanced datasets. Another problem often neglected is that the final accuracy is the result not only of the accuracy of the model but also depends on the prior probability of the class under investigation.
ML uses evaluation metrics mainly addressing accuracy in classification such as Accuracy, area under the curve AUC , etc. By contrast, statistical metrics are different and more linked to inference p -values and more recently focusing on reporting effect sizes e.
One problem that requires to be addressed when complementing statistical analysis with ML results is in the comparison between the metrics used in statistics e. Salgado addressed the problem of translating performance indicators from ML metrics and statistical metrics.
It is possible to transform the accuracy results obtained from ML models to more psychologically oriented effect size measures Salgado, Using results from Table 1 an out-of-sample accuracy of However, an accuracy of One procedure which is believed to be at the origin of lack of replicability in reporting experimental results, analyzed with statistical inference, is the so called p-hacking Nuzzo, In ML analyses, there is a similar source of lack of replicability, which could be called model hacking.
If many models are tested in order to report only the best model, we are in a condition similar to p- hacking. In the example reported in Table 1 , using cross validation and reporting only the best performer among the classifiers, in this case SVM, would have produced an accuracy estimation in excess of 4.
In order to avoid model hacking, one strategy is to verify that classification accuracy is not changing much among different classes of classifiers see Monaro et al. Additionally, model stability may be addressed by combining different classifiers into an ensemble classifier that indeed reduces the variance in out-of-sample predictions and therefore gives more reliable predictions.
Using ensembles instead of specific classifiers is a procedure that avoids model-hacking. We have highlighted, in this paper, the reasons why ML should systematically complement statistical inferential analysis when reporting behavioral experiments.
Advantages derived from using ML modeling in an analysis experimental results include the following:. Known potential pitfalls of ML data analysis that may obstacle a more extensive use of the ML methods are:. When only the single best performer model is reported rather than a variety of models with differing theoretical assumptions. Model hacking may lead to an overestimation of replicable results.
A remedy against model hacking consists in reporting many ML models or ensemble models;. Usually maximum accuracy in prediction is achieved with highly complex non-interpretable models such as XGboost, Random Forest and Neural Networks. This is probably the single most important problem in clinical applications where the clinician needs a set of workable rules to drive the diagnosis.
To tamper the problem it may be useful to report simple decision rules that may help in evaluating the cost of non-interpretability accuracy achieved with simple interpretable models as compared to maximum accuracy achieved by complex less interpretable models. Interpretability is important in clinical setting where clinicians need simple and reliable decision rules see Figure 3 in Mazza et al.
The datasets analyzed in this article are not publicly available. Requests to access the datasets should be directed to giuseppe. GO devised the main research topic, and planned and carried out the ML analysis. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Aha, D. Instance-based learning algorithms. Anderson, J. Neurocomputing: Foundations of Research.
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Using the classification scheme he pioneered, Dr. Millon guides clinicians through the intricate maze of personality disorders, with special attention to changes in their conceptualization over the last decade. Extensive new research is included, as well as the incorporation of over 50 new illustrative and therapeutically detailed cases.
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