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I am doing an analysis of various factors that determine whether a patient is likely to have an illness. I will do this using multiple linear regression.

I have noted that some papers perform a univariate analysis first (whether this is correct or not is not the purpose of this question) to determine/ reject factors that may be used in the multiple regression.

What I don't understand is whether the univariate analysis should be a univariate regression analysis or whether it should be the appropriate difference in populations (eg Chi-squared/ t-test etc depending on variable type).

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  • $\begingroup$ What is your outcome variable? Is it something like Y = 1 if patient has the illness and 0 otherwise? If yes, you would need to perform a logistic regression. Usually people perform the univariate analyses using the tests you mention. But it's fine to use univariate regressions instead. $\endgroup$ Dec 1, 2018 at 16:52
  • $\begingroup$ The outcome is binary. So I guess I would use regression. So in other words binary outcome vs continuous input means regression. Ok got it.... $\endgroup$ Dec 1, 2018 at 17:02
  • $\begingroup$ Regression is a general term so you need to be specific when specifying the nature of the regression model for cross-sectional data. If you have a continuous outcome (e.g., blood pressure), then you would use a 'linear regression model'. If you have a count model (e.g., number of days free of pain), you would a 'count regression model'. If you have a binary outcome, then you would use a 'binary logistic regression model'. $\endgroup$ Dec 1, 2018 at 17:07
  • $\begingroup$ If you have a categorical outcome whose categories don't follow a natural order (e.g., Treatment preference, with categories Treatment A, Treatment B, No Preference), you would use a 'multinomial regression model'. If you have a categorical outcome with ordered categories (e.g., level of pain, with categories 1 = low through 3 = high), you would use an 'ordered logistic regression'. Again, this terminology assumes that you collected data on your subjects at a single time point. $\endgroup$ Dec 1, 2018 at 17:14

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Assuming that Y is continuous (rather than binary) and the first predictor X1 is binary, you could perform either of the following:

1. A t-test which allows you to compare the mean value of Y when X1 = 1 against the mean value of Y when X1 = 0;

2. A simple linear regression model regressing Y on X1.

I am guessing most people use a t-test because it has the flexibility of allowing the variability of the Y values when X1 = 0 to be different from the variability of the Y values when X1 = 1. But if that needs to be allowed for, it can easily be accommodated in the context of a simple linear regression model too by allowing the error variance to depend on the values of X1.

Assuming that Y is continuous and the second predictor X2 is categorical with k categories, where k > 2, you could perform either of the following:

i. A one-way analysis of variance, which allows you to compare the mean value of Y when X1 = 1 across the categories of X2;

ii. A simple linear regression model regressing Y on X2. (When fitted to the data, this model will actually include k - 1 dummy variables as predictors, all of which help encode the effect of X2 on Y.)

By default, the one-way anova in i. and the simple regression model in ii. assume that the variability of the Y values is roughly the same across the categories of the X2 variable. If that is not the case, each of these methods can be modified accordingly.

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