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From the updated descriptionn : you have repeated measures within Subject and you have 52 subjects. It does not make sense to fit this as a fixed effect. It should be a grouping variable in the random structure. Random is "a variable that describes a certain characteristic of an individual. It can be one of 3 options". As such it does not make ...


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I realize that when I use LASSO to select a model, I can't infer from it because it penalizes the coefficients to best fit the data. I'm just a little confused as to what exactly this means. Isn't this also what a regression does? It tries to fit the data best possible? If I can't infer from a LASSO model, what do I use it for? LASSO is like OLS plus ...


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It makes sense. It is more common however to keep the training and test sets separated. So that you train your model on the train set, and then predict on the test set alone. From there you can calculate the prediction error, and a $R^2_{pred}$ if you like. (train on $n$ data points, evaluate on $p$ data points, in your terms.) You can also look up stuff ...


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I'm not familiar with the details of Keras specifically, but I see that your output is one node with softmax activation. The $i^{\mathit{th}}$ element of softmax on a preactivation vector $a$ of length $n$ is: \begin{align} \text{softmax}(a)_i & = \frac{\exp(a_i)}{\sum_{i=1}^n \exp(a_i)} \end{align} If $n=1$, we get: \begin{align} \text{softmax}(a)_1 &...


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It makes sense to apply $R^2= 1-{\sum(y_i-\hat y_i)^2}/{\sum(y_i-\bar y)^2}$ to test set directly. It's a measure of the size of squared residuals compared to the variance of true values. Alternatively, if you adopt the notion of deviance (see this answer), then you might use the null model from training data instead: $$\tilde R^2= 1-\frac{\sum(y_i-\hat y_i)^...


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You can workout the integral by noting that $p(t)$ is the marginal distribution between $p({\bf w})$ and $p(t\vert{\bf w})$. More specifically, if you refer to page 93 of the book, it says Given a marginal Gaussian distribution for $\bf x$ and a conditional Gaussian distribution for $y$ given $\bf x$ in the form $$p({\bf x}) = \mathcal{N}({\bf x} |\...


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To me, it seems that when the model is making a prediction for subject $s$ at time $t$, it should be allowed to use as training data the observations from all subjects other than $s$ and from all of $s$'s observations that occurred earlier than $t$. This approach may (may!) make you overestimate your accuracy, depending on your actual use case. And that in ...


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You are asking about the class of algorithms or models known as (recursive|online|incremental|streaming) (estimation|regression|forecasting|learning) algorithms. Generally, I see the terms "recursive regression", "incremental learning", "streaming (machine) learning" or "online learning" used most frequently. Online ...


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Model selection criteria, such as the BIC, the AIC, or the minimum length criterion, are commonly used in the literature, so nobody would laugh and point at you if you use them (and if they do, please reconsider your acquaintance). However, the validity of these criteria rely on some strong assumptions, that you will need to verify and justify. For instance, ...


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There is likely to be nonlinearity involved here. I would approach this by trying to find some theoretical material that builds a mathematical model with the variables, and go from there. You could also consider a GAM model. In general stepwise procedures are not a good idea, especially where you have nonlinear and/or interaction terms.


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Stepwise is a bit unnecessary. Your predictor space is small enough (p=4) that you could do best subsets regression. Also, when exploring interaction effects check out lower order interaction terms. High order interactions like the one you listed arent often explored, unless there is a very very strong expert recommendation. For the purposes of your report I ...


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