2. Materials and methods
fits
REGRESSION
The development of the DS-TOFHLA was based on the D-TOFHLA [Motivated by a need to reduce the administration time and create an easier-to-use screening instrument, a short version of the original full-length American TOFHLA was designed: the S-TOFHLA [The development of the DS-TOFHLA was based solely on an algorithm-based selection of variables and multiple linear regression (MLR). The classical method to obtain an unbiased evaluation, when building and testing models, is to have separate training and testing datasets, which can be accomplished by splitting a given dataset into a training set and a test set. In smaller datasets K-fold cross-validation is often used, which makes it possible to use almost the whole dataset for both training and testing while still avoiding bias. The present study used a special form of K-fold cross-validation, the Leave-one-out cross-validation (LOOCV), where K is set to the number of samples (K = N). LOOCV can be particularly useful when working with small datasets (as in our case, n = 158) because it allows for a more reliable estimate of the model’s performance. With a small dataset, there is a higher risk of overfitting, which occurs when a model is too complex and fits the training data too closely, resulting in poor generalization to new data. LOOCV helps to mitigate this risk by repeatedly training the model on slightly different subsets of the data, allowing for a more robust evaluation of its performance. LOOCV also ensures the best possible use of the dataset (i.e., 100% of the dataset is used as training data and 100% as test data) [The quality goal in the development of the DS-TOFHLA was expressed by two conditions. First, Pearson’s correlation coefficient between the DS-TOFHLA score (i.e., the predicted Danish TOFHLA total score) and the D-TOFHLA score should be at least 0.9 (r ≥ 0.9 being indicative of a very strong correlation). Second, if possible, the model should not contain numeracy items to eliminate the involvement of an interviewer.