I've only taken a few statistics courses, and so I apologize if any of my questions are rudimentary, however, I'm wondering if someone could explain/direct me to resources regarding the correct process of testing model assumptions, model fitting, and also the consequences behind not meeting model assumptions such as normality, homoscedasticity, etc?
My impression is that it's important to meet model assumptions because otherwise, the mathematics of the models will not work. However, this link, caught my eye in that it seems to explain that you can still estimate parameters, and though it's not ideal for hypothesis testing (is this assessment of p-value?), you can get around this with bootstrapping.
Is this true in both OLS and in linear mixed effects modeling where you have to account for random effects? Additionally, someone suggested to me that it's not practical in real life settings to meet all the assumptions because data is rarely perfect (ie: not always normally distributed, has a lot of variance, etc). My understanding is if the data isn't meeting assumptions, that suggests it's the wrong model and using the model just leads to inaccurate results. Is this true, or in real life settings of analysis, are model assumptions rarely ever met? This doesn't seem true to me, though in my own experience, I have been having difficulty meeting many assumptions or rectifying them with transformations, which makes it hard for me even proceed in my analyses.
Any thoughts/advice on this to clear things up would be very appreciated.