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I am very unfamiliar with approaching regressions of discrete observations when there are multiple discrete outcomes, and am further befuddled when ordinality and proportions are involved. If I were to want to predict changes in proportions of ordinal events over time (let's suppose a concrete example of predicting changes corresponding to risk factors in accident severity proportions at a work site where accidents are classed as minor, major, extreme, and fatal), what approaches should I be looking at? Thank you for your help!

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