Is it mandatory to subset your data to validate a model? I'm having a hard time getting on the same page as my supervisor when it comes to validating my model. I have analyzed the residues (observed against the fitted values) and I used this as an argument to discuss the results obtained by my model, however my supervisor insists that the only way to validate a model is to make a random subset of my data, generate the model with 70% of it and then apply the model on the remaining 30%.
The thing is, my response variable is zero inflated (85% of it, to be more rpecise) and i prefer not to create a subset as it is already very difficult to converge to a result. 
So, my question is: what are the possible (and scientifically acceptable) ways to validate a model? Is subsetting data the only way? If possible, reference your questions with articles/books so I can use it as an argument when presenting my alternatives.  
 A: To start, I would suggest that it is usually good to be wary of statements that there is only one way to do something. Splitting an obtained sample into a "training" and a "testing" data set is a common approach in many machine learning/data science applications. Oftentimes, these modeling approaches are less interested in hypothesis testing about an underlying data generation process, which is to say they tend to be somewhat atheoretical. In fact, mostly these sorts of training/testing splits just want to see if the model is over-fitting in terms of predictive performance. Of course, it is also possible to use a training/testing approach to see if a given model replicates in terms of which parameters are "significant," or to see if the parameter estimates fall within expected ranges in both instances. 
In theory, validating or invalidating models is what science, writ large, is supposed to be doing. Independent researchers, separately examining, generating, and testing hypotheses that support or refute arguments about a theory for why or under what circumstances an observable phenomenon occurs - that is the scientific enterprise in a nut shell (or at least in one overly long sentence). So to answer your question, to me, even training/testing splits are not "validating" a model. That is something that takes the weight of years of evidence amassed from multiple independent researchers studying the same set of phenomena. Though, I will grant that this take may be something of a difference in semantics about what I view model validation to mean versus what the term validation has come to mean in applied settings... but to get back to the root of your question more directly. 
Depending on your data and modeling approach, it may not always be appropriate from a statistical standpoint to split your sample into training and testing sets. For instance, small samples may be particularly difficult to apply this approach to. Additionally, some distributions may have certain properties making them difficult to model even with relatively large samples. Your zero-inflated case likely fits this latter description. If the goal is to get at an approximation of the "truth" about a set of relations or underlying processes thought to account for some phenomenon, you will not be well-served by knowingly taking an under-powered approach to testing a given hypothesis. So perhaps the first step is to perform a power analysis to see if you would even be likely to replicate the finding of interest in your subsetted data. If it is not appropriately powered, that you could be an argument against the testing/training split. 
Another option is to specify several models to see if they "better" explain the observed data. The goal here would be to identify the best model among a set of reasonable alternatives. This is a relative, not an absolute, argument you'd be making about your model. Essentially, you are admitting that there may be other models that could be posited to explain your data, but your model is the best of the tested set of alternatives (at least you hope so). All models in the set, including your hypothesized model, should be theoretically grounded; otherwise you run the risk of setting up a bunch of statistical straw men. 
There are also Bayes Factors in which you can compute the weight of evidence your model provides, given your data, for a specific hypothesis relative to alternative scenarios. 
This is far from an exhaustive list of options, but I hope it helps. I'll step down from the soapbox now. Just remember that every model in every published study about human behavior is incorrect. There are almost always relevant omitted variables, unmodeled interactions, imperfectly sampled populations, and just plain old sampling error at play obfuscating the underlying truth.    
A: I think the answers here diverge because the question is somewhat unclear, foremost: what do you mean by "validation"?
A 70/30 split (or a cross-validation for that matter) is usually performed to assess the predictive performance of a model or an entire analysis chain (possibly including model selection). Such a validation is particularly important if you are comparing different modelling options in terms of their predictive performance. 
It's another case entirely if you don't want to select models, and are also not interested in predictive performance as such, but you are interested in inference (regression estimates / p-values), and want to validate if your model / error assumptions of the GLMM are adequate. In this case, it would be possible to predict to the hold-out and compare predictions to observed data, but the by far more common procedure is to do a residual analysis. If you need to prove this to your supervisor: this is basically what every stats textbooks teaches to do right after linear regression. 
See here for how to run a residual analysis for GLMMs (including zero-inflation with glmmTMB, which I would prefer over glmmadmb) with the DHARMa package (disclaimer: I am the maintainer).  
A: The short answer is yes, you need to assess your model's performance on data not used in training. 
Modern model building techniques are extremely good at fitting data arbitrarily well and can easily find signal in noise. Thus a model's performance on training data is almost always biased.
It is worth your time to explore the topic of cross validation (even if you are not tuning hyperparameters) to gain a better understanding of why we hold out data, when it works, what assumptions are involved, etc. One of my favorite papers is:
No unbiased estimator of the variance of k-fold cross-validation
A: Data splitting is in general a very non-competitive way to do internal validation.  That's because of serious volatility - different 'final' model and different 'validation' upon re-splitting, and because the mean squared error of the estimate (of things like mean absolute prediction error and $R^2$) is higher than a good resampling procedure such as the bootstrap.  I go into this in detail in my Regression Modeling Strategies book and course notes.  Resampling has an additional major advantage: exposing volatility in feature selection.
