How about google (there are tons of helpful pages, especially for R codes) or a good textbook for GLM, e.g. Peter K. Dunn - Generalized Linear Models With Examples in R, Springer?

Rainer Duesing ,thank you for your response and recommendations. I have seen some of the pages. especially this one below was very helpful.

https://stats.stackexchange.com/questions/187100/interpreting-glm-model-output-assessing-quality-of-fit

But, I need more realistic and sound answers from scientific community.

This forum is not suiteable to teach you statistics. Your question is so broadly formulated that it is not clear where to start at which level (e.g. do you already know the concept of information criteria like AIC or do you need to learn this, yet; are you already familiar with residuals in general or not?). There are whole chapters in textbooks dedicated to explain these parameters, therefore it is not possible to explain it to you in this forum with a couple of sentences or paragraphs. There is no shortcut to learn these things.

Dear,Rainer Duesing ,I think you are right. I have to ask you in short and specific way.

As we know the model which has a less Akaike-Information-Criterion-(AIC) value is better than the other higher value. The Akaike information criterion (AIC) is an estimator of the relative quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model, relative to each of the other models. Thus, AIC provides a means for model selection.

However, unlike adjusted R-squared, the number itself is not meaningful. If you have more than one similar candidate models (where all of the variables of the simpler model occur in the more complex models), then you should select the model that has the smallest AIC.

In other case, Deviance is a measure of goodness of fit of a model. Higher numbers always indicates bad fit. The null deviance shows how well the response variable is predicted by a model that includes only the intercept (grand mean) where as residual with inclusion of independent variables.

Fisher’s scoring algorithm is a derivative of Newton’s method for solving maximum likelihood problems numerically. This doesn’t really tell me a lot that i need to know, other than the fact that the model did indeed converge.

My concern was , there are outputs for one model only such as

----->Deviance Residuals:

Min 1Q Median 3Q Max

----->Null deviance:

----->Residual deviance:

----->AIC:

----->Number of Fisher Scoring iterations:

and also there are output values in case of comparison using chi-square analysis such as deviance difference for both models.

Analysis of Deviance Table

Model 1: output ~ input 1 + iput 2 + input 3

Model 2: output ~ input 1 + iput 2 + input 3 + input 4

Resid. Df Resid. Dev Df Deviance Pr(>Chi)

1 417 488.96

2 409 466.88 8 22.074 0.00478 **

My question is how the residual deviance and its difference in comparison case will influence the decision in my model interpretation.

Even if the smallest value of deviance will be acceptable, what will be the minimum required and acceptable value as a whole study. I hope you got my question even if it was shallow in my first post.

There is no overall minimum value with which you can decide, if the model fits or not. It is not possible to determine such a value (even with the classic R^2: which value is high/low enough for a good/bad model? --> it depends on the context and research question/area). Even if you compare several models with each other and choose the one with the lowest AIC, it only says that it is the best fitting model of the models you chose in the first place. It is not a measure of the global optimum, but the local one, so to speak.

In my opinion, it is useful if not necessary to think about your data and plausible assumptions about the data generating process to choose an appropriate model. Visualization can and should be very helpful. Plot your data against your model. How does the model represent the data and mean value structure? How are the residuals distributed around the implied model? For which of the models you have chosen is the fit of theoretical implication and visual inspection most plausible?

It is something I struggle with myself, when looking at the data, to be honest. But I have not heard of any "overall" solution for it, which tells you exactly which model is best. The distribution of the residuals is also a good indicator of model fit. Look at them directly, plot them, do not only rely on the numbers provided by the output.

Maybe there are some further advices from other people here?

Thank you very much,dear Rainer Duesing . I appreciate all your answers.

Still, Plot observation will be judgmental and difficult for different data nature of variables such as a combination of categorical and continuous data nature. Because, when we look plot observation, different patterns show a different representation and this will be difficult to be sure in one scientific interpretation.

Do you think overlay(the same pattern) of the plot between the data and calibrated model is a good sign of fit?

In addition to this, the tests like adjusted R-squared will show the residuals distribution around the given model to some extent as plot. But, there is no a definite test for goodness of fit for the case of glm model estimation which has binary and more response.

Some suggests to use , Hosmer-Lemeshow Goodness of Fit, for binary data to implement a goodness of fit test.The model appears to fit well as there is no significant difference between the model and the observed data (i.e. the p-value is above 0.05).As with all measures of model fit, we’ll use this as just one piece of information in deciding how well this model fits.

But, The draw back of Hosmer-Lemeshow Goodness of Fit, It doesn’t work well in very large or very small data sets, but is often useful nonetheless.

Finally, I need to ask you some questions if you are familiar with such plotting techniques.

-->which packages were you employed for plot in R?

-->what kind of plotting techniques were give you viable information?

--> How do you check that the plotting value was shown in accurate way?

-->how will you treat un-captured errors beyond residual errors for such complex models in case of visualization?

Thank you

Dear Mollalign Yizengaw,

I will have a look at my scripts, when I am back at my office tomorrwo, maybe I can give you some more information for the questions you asked. I will do my best.

Best,

Rainer

In case of a binary logistic regression it is possible to calculate different pseudo R^2 values, which might help to assess the model fit, i.e. Cox & Snell's Rsquared, Nagelkerke's Rsquared or Hosmer & Lemeshow's Rquared. All have different values and slightly different interpretations. Additionally, you should have a look at the (over-)dispersion with the dispersion parameter phi, which is the ratio of dispersion/df.

For plotting in R I do not use any "special" packages. There are some routines I do to get an impression of the data. Mostly I follow the Dunn & Smyth (chapter 8) book I mentioned already above, to check assumptions and the model itself of a generalized linear model. For the systematic component: I use deviance residuals and quantile residuals, plot them againts the predictors with LOESS curve to detect trends, check working responses, partial plots; for the random component: QQ plot, distribution of the deviance residuals, residuals vs predicted values, outlierdetection and influential cases with Cooks distance and leverage values. Additionally I use the Pregibon test and the Hosmer-Lemeshow goodness of link(!) test, although both are not always recommended, as well as if there is any linear relationship between residuals and the predictors.

I think that is what I do to get an overview and an impression of the data.

If you are looking for other helpful display functions and possibilities, I can recommend the book Heiberger & Holland - Statistical Analysis and Data Display (using R's lattice package) and the DHARMa package, https://cran.r-project.org/web/packages/DHARMa/index.html for residual diagnostics for hierarchical regression models.

thank you dear Rainer Duesing

You are welcome!