Mnlogit R

[Lavonna Baldree]

Ihave question regarding the mnlogit package in R which I'll ask on StackOverflow as it's related to a specific language and library, however I won't be offended if someone decides to move it to Cross Validated (it was a hard choice of which StackExchange site was most appropriate).

I'm just trying to make sure I understand how this works, since the documentation isn't too detailed, I see some confusing/conflicting blog entries on this package, and because it's been a couple of years since I've dealt with choice models.

To try to clarify my understand I read an R-Bloggers article on the topic. It actually made things more confusing by repeating the Fish example, but with a preamble describing the dataset in this way:

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In my current project on Long-term care at some point we were required to use a regression model with multinomial responses. I was very surprised that in contrast to well-covered binomial GLM for binary response case, multinomial case is poorly described. Surely, there are half-dozen packages overlapping each other, however, there is no sound tutorial or vignette. Hopefully, my post will improve the current state.

We can distinguish two types of multinominal responses, namely nominal and ordinal. For nominal response a variable can possess a value from predefined finite set and these values are not ordered. For instance a variable color can be either green or blue or green. In machine learning the problem is often referred to as a classification. In contrast to nominal case, for ordinal repose variable the set of values has the relative ordering. For example, a variable size can be small According to Agresti (2002) we can the problem can be formulated by two similar approaches: through baseline-category logits or multivariate GLM. In general, these two approaches are equivalent with identical maximum-likelihood estimates, the only thing which is different is the formula representation.

The baseline-category logits is implemented as a function in three distinct packages, namely nnet::multinom() (referred as to log-linear model), mlogit::mlogit, mnlogit::mnlogit (claims to be more efficient implementation than mlogit, see comparison of perfomances of these packages).

Nice thing about this package is that it allows for using different link functions, i.e. "logit", "probit", "cloglog", "loglog", and "cauchit". To my regret I know only "logit" and "probit" from this list.

Perhaps, now you have a question which package to use? Well, I do not know, just choose one and stick to it. I will use probably VGAM, as long as it covers various models and seems like nicely documented.

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The highly contagious SARS-CoV-2 virus has led to significant morbidity and mortality worldwide1. Pneumonia is regarded as one of the main complications of COVID-19 disease, which can lead to lethal conditions while escalating the cost of healthcare2. The most popular diagnostic test considered as the gold standard for coronavirus disease is the reverse transcription polymerase chain reaction (RT-PCR) assay3. While highly specific, RT-PCR has shown low sensitivity, as studies have reported significant false-negatives in patients who had abnormalities in their chest CT images confirmed with secondary follow-up RT-PCR to be positive for COVID-194.

CT aids in the diagnosis and management of COVID-19 patients and could be potentially used as an outcome/survival prediction tool, towards enhanced treatment planning5. CT scanning has been utilized as a highly sensitive tool for COVID-19 diagnosis6 since it is fast and generates quantifiable features (e.g., the extent to which lung lobes are involved) and non-quantifiable features (e.g., ground-glass opacities and their laterality) to assess COVID-19 pneumonia, besides the enhanced sensitivity compared to RT-PCR7.

There has also been a growing interest in using imaging data of patients, such as thoracic CT images. For example, a study by Sanders et al.13 computed the score of CT images in patients with cystic fibrosis and evaluated the prognostic ability. A promising line of research that emerged recently reported on the CT severity index and its correlation with acute pancreatitis severity14,15,16. The COVID-19 Reporting and Data System (CO-RADS) was suggested for standardized visual assessment of COVID-19 pneumonia to enhance agreement between radiologists17. This system includes features for the diagnosis of COVID-19 and consists of a 6-point scale for categorizing patient CT images. In addition, other guidelines aiming to reach consensus when interpreting COVID-19 suspected chest CT images were proposed18. These guidelines are mostly based on visual assessment of images; e.g. the amount to which lung lobes are involved, the volume of which is infected, and anatomical assessments.

Francone et al.19 reported a study on the correlation between CT score and the severity of coronavirus disease. Zhao et al.20 also conducted research on the measurement of the extent to which lung lobes are infected and evaluation in COVID-19 patients' prognosis. Li et al.21 also confirmed the association between chest CT score and COVID-19 pneumonia severity. At the same time, most scoring systems involve visual assessment and hence are time-consuming20,21. In this regard, medical image analysis using machine learning (ML) and radiomics has been applied to quantify features to tackle these main challenges22.

The field of radiomics opens pathways for the study of normal tissues, cancer, cardiac disease, and many other diseases, including potentially the newly emerging COVID-19 disease23,24,25,26,27,28,29,30. Specifically, Xie et al.31 evaluated the potential of a radiomics framework to diagnose COVID-19 from CT images. Di et al.32 also studied whether radiomics features can help to distinguish between pneumonia of COVID-19 and that of other viral/bacterial causes. A number of studies reported on the application of radiomics analysis to CT images towards COVID-19 classification and prognostication33,34,35,36. Homayounieh et al.37 assessed the prognostic power of CT-based radiomics features to determine severe and non-severe cases. In another study, Li et al.38 proposed a radiomics model based on CT images and classified patients based on the criticality of their disease. A recent study by Yip et al.39 applied a robust radiomics model to CT images to predict the severity of COVID-19 disease in patients. All above models pursued binary task performance, which reduced multiclass classification to two class approaches. However, in the real clinical triage situation, scoring systems consist of multi-class datasets. In the present study, involving a large cohort of patients, we aimed to construct a CT radiomics-based multi-class classification model to predict the severity of COVID-19 pneumonia.

All CT images were automatically segmented using a deep learning-based algorithm for whole lung segmentation42. After whole-lung 3D segmentation, all images were reviewed and modified to ensure correct 3D-volume lung segmentation.

In this study, we used two different feature selection algorithms, including Bagging Random Forests (BRF) and Multivariate Adaptive Regression Splines (MARS)46. BRF and MARS algorithms were implemented in "VSURF" and "earth" R packages, respectively. Importance values (IVs) were calculated using generalized cross-validation criterion with normalization. For multiclass classification, we implemented multinomial logistic regression (MLR) using the "mnlogit" R package. The MLR model fitness indices included p value of the Wald test (corrected for false-discovery rate via Benjamini and Hochberg method), pseudo R2, as well as Akaike information criterion (AIC, goodness of fit indices in generalized linear regression models). In the MLR model, class 0 served as a reference class whereas statistical comparison between two predictive models was performed by the Likelihood Ratio Test.

Table 1 summarizes the selected features and their relative importance value by BRF and MARS for multiclass classification. These features were selected in train/validation sets using nested cross validation and grid searches. Twenty-three radiomic features were selected by BRF, including 11 from first-order, 9 from GLCM, 1 from GLRLM, 1 from GLDM, and 1 from shape features. Among these features, Correlation (IV: 100%) and Cluster Tendency (IV: 88%) from GLCM, Mean Absolute Deviation (IV: 80%), Robust Mean Absolute Deviation (IV: 72%) and variance (IV: 70%) from first-order features were selected as the most important ones. In the MARS algorithm, 10 features were selected with high IVs, including 2 from first-order, 1 from GLDM, and 1 from GLCM. The highest IV was achieved by mean absolute deviation (IV: 100%) and skewness (IV: 55%) from first-order, Gray Level Variance from GLDM (IV: 53%), and Correlation from GLCM (IV: 54%). The mean absolute deviation, skewness, variance from first-order, flatness from shape, cluster prominence from GLCM features, and Gray Level Non Uniformity Normalize from GLRLM were selected by both BRF and MARS algorithms. Figure 3 depicts the feature map of different radiomics features in different classes (10Precentile from first order, Gray level Non-Uniformity Normalized from GLRLM, Idm from GLCM and Zone Entropy from GLSZM).

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