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Attempts have been made to asses the accuracy of various pseudo R-squareds by predicting a continuous latent variable through OLS regression and its observed binary variable through logistic regression and comparing the pseudo R-squareds to the OLS R-squared.
Pseudo-R-squared values are used when the outcome variable is nominal or ordinal such that the coefficient of determination R 2 cannot be applied as a measure for goodness of fit and when a likelihood function is used to fit a model. In linear regression, the squared multiple correlation, R 2 is used to assess goodness of fit as it represents ...
In R, the glm (generalized linear model) command is the standard command for fitting logistic regression. As far as I am aware, the fitted glm object doesn’t directly give you any of the pseudo R squared values, but McFadden’s measure can be readily calculated.
The pseudo-$R^2$, in logistic regression, is defined as $1 - \frac{L1}{L0}$, where $L0$ represents the log likelihood for the "constant-only" model and $L1$ is the log likelihood for the full model with constant and predictors.
We have seen from our previous lessons that Stata’s output of logistic regression contains the log likelihood chi-square and pseudo R-square for the model. These measures, together with others that we are also going to discuss in this section, give us a general gauge on how the model fits the data.
How to use R-squared, Adjusted R-squared and Pseudo-R-squared to evaluate the goodness of fit of Linear and certain Nonlinear regression models. One of the most used and therefore misused measures in Regression Analysis is R² (pronounced R-squared).
R squared is a useful metric for multiple linear regression, but does not have the same meaning in logistic regression. Statisticians have come up with a variety of analogues of R squared for multiple logistic regression that they refer to collectively as “pseudo R squared”.
7.4.2 Pseudo-R-squared. A more useful statistic to evaluate goodness of fit in logistic regression is a variant of \(R^2\) called Pseudo-\(R^2\), which we calculate individually for each logistic regression model using the residual deviance and null deviance, as follows. \(\text{Pseudo-R}^2 = 1-\frac{\text{residual deviance}}{\text{null ...
Psuedo r-squared for logistic regression. In ordinary least square (OLS) regression, the R 2 statistics measures the amount of variance explained by the regression model. The value of R 2 ranges in [0, 1], with a larger value indicating more variance is explained by the model (higher value is better). For OLS regression, R 2 is defined as ...
Pseudo r-squared is a set of statistics used to provide a measure of goodness-of-fit for models that do not fit the assumptions of traditional linear regression, particularly in the context of logistic regression models.