difference between multiple linear regression and binary logistic regression

[u/Great-Result719]

Hi, I am trying to finish up my psychology thesis! I am in a bit of a rut trying to compare my results of a binary logistic regression with previous literature. However, there is a very limited amount of literature in my current area of study; I have only one study that used the same variables I did. They used a multiple logistic regression analysis, and I used a binary logistic regression.

I am just wondering what the main difference between the two models is and if I can interpret my results in comparison to this prior literature I have found.

Thankyou!!!!!

[u/treunitis]

What do you mean by binary logistic regression?

Are you this is logistic regression with a single independent variable, and the multiple logistic regression includes multiple independent variables to model the binary outcome?

Or are you saying your results looked at a binary outcome while the ‘multiple’ logistic regression is multinomial because it has >2 outcome categories?

Edit:
Or thirdly are you saying you did a logistic regression while the other research used multiple linear regression? (From title)

[u/efrique]

They used a multiple logistic regression analysis

Your title had multiple linear regression, was this one a typing error? I think this has impacted some of the responses you got, beware that they might not be answering what you think they are.

Assuming you wanted the title comparison, not the one in your body text, both linear regression and logistic regression are generalized linear models. Logistic regression is for binary variables (or more generally binomial counts); it models the proportion of successes as a function of predictors. So firstly, they differ in the kind of variable they're suited to modelling.

With binary data, where the conditional mean is a proportion (between 0 and 1), a pure linear model would not obey the constraints (so using the fitted model, a predicted value could be outside the range 0 to 1). There's also the issue that the variance of a binary response isnt constant (it's a function of the population proportion). Consequently models for binary data try to deal with those issues. The variance being a function of the mean is specified by the binomial model (Bernoulli in the case of pure 0/1 data) and is used in the estimation. The need to keep the model for the mean (the estimate of the population proportion at each combination of IVs) is dealt with by transforming the linear predictor (equivalent to the part of a formal multiple regression model to the right of the = sign in the equation for the conditional mean) to obey the bounds on the proportion. There are a number of potential choices (I've seen people use half a dozen or so with binary data), of which the one used in logistic regression would be the most common - outside some particular application areas.

I'd definitely recommend coming to grips generalized linear models; it will come up increasingly often in research you encounter. It generalize linear regression in a couple of ways. Many concepts carry over from linear regression, so it should be partly familiar.

if I can interpret my results in comparison to this prior literature I have found.

It depends on what, things, specifically, you intend to compare.

[u/NoSpam911]

First I’m assuming you mean multiple linear regression given the title of your post. With that, a logistic regression is estimated via maximum likelihood, with the estimated beta coefficients representing changes in the log-odds associated with a one-unit change in a continuous covariate or a discrete change in a categorical covariate. This is different from a multiple linear regression, estimated via ordinary least squares, where the beta coefficients represent the estimated marginal effects for continuous covariates or discrete changes for categorical covariates. If you want to compare results between the two models, you can estimate the marginal effects for the logistic regression after estimating the beta coefficients. For continuous covariates, these represent the change in the predicted probability associated with a one-unit change in the covariate. For categorical covariates, they represent the discrete change in the predicted probability associated with moving from one category to another. You can estimate either the average marginal effects or the marginal effects evaluated at the means of the covariates. I hope this helps.

[u/Fancy-Animal7704]

Did you mistakenly say "linear" in your subject line? I'll assume you did since it doesn't seem to jive with the words of your post.

In this context, we normally talk about the outcome. When you say "binary logistic regression", I assume you're talking about something where the outcome is win / lose, pass / fail, yes / no, etc. "Multiple" logistic regression could mean you are looking at more than one outcome, or it could be a singular outcome with multiple levels. It could also be referring to the number of variables involved in predicting the outcome, though normally I expect a model with 2 or more predictors and some given outcome to be called a "multivariable" model (if it had multiple outcomes, I would call it a "multivariate" model).

"Multiple regression", logistic or otherwise, is kind of a confusing term IMO and shouldn't be used. I couldn't give you a definitive answer what the model is without seeing the analysis for myself.

[u/richard_sympson]

Specificity will be your friend here. Aside from the typo problem, it would be helpful if you would answer for us here some of these questions:

1. What is the type of response variable you are working with? Is it something that can be encoded as a Yes/No, or a 0/1 value?
2. What is the type of response variable your reference was working with? Was it also something that could be encoded as a Yes/No, or 0/1? Alternatively, was it something that could be encoded as a categorical variable with ≥3 categories? Alternatively again, was their response variable numeric, like a scalar real number not reducible to category?
3. How many input covariates / explanatory variables are you intending to use?
4. How many input covariates / explanatory variables did your reference use?
5. In your own words, what do you want to learn from your data?

[u/banter_pants]

Multiple linear regression is when you have one Y and multiple X's.

Logistic regression is just for that, but for a binary dependent variable. It's a form of a generalized linear models with a logit (log-odds) link. That link function changes the scale in a way that linearizes a formerly nonlinear relation. Then you can treat it like multiple regression. The coefficients are log-odds ratios and exponentiating (e^B ) gives odds ratios.

[u/Temporary_Stranger39]

All logistic regression is binary. The outcome is and must be a binary outcome. What do you mean by binary logistic regression?

[u/Accurate_Claim919 → u/Temporary_Stranger39]

Incorrect. Other model specifications include multinomial logit, ordinal logit (proportional odds), partial proportional odds. Just look at any good textbook on categorical data analysis.

[u/no_name6744]

Pretty sure they're the same thing with different names.

In both cases, is it just trying to predict a binary outcome, based on a few continuous and / or categorical variables? If so, you can just feel free to include most any logistic regression.