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SN Ia cosmology depends on the ability to fit and standardize observations of supernova magnitudes with an empirical model. We present here a series of new models of SN Ia spectral time series that capture a greater amount of supernova diversity than is possible with the models that are currently customary. These are entitled SuperNova Empirical MOdels (SNEMO; https://snfactory.lbl.gov/snemo). The models are constructed using spectrophotometric time series from 172 individual supernovae from the Nearby Supernova Factory, comprising more than 2000 spectra. Using the available observations, Gaussian processes are used to predict a full spectral time series for each supernova. A matrix is constructed from the spectral time series of all the supernovae, and Expectation Maximization Factor Analysis is used to calculate the principal components of the data. K-fold cross-validation then determines the selection of model parameters and accounts for color variation in the data. Based on this process, the final models are trained on supernovae that have been dereddened using the Fitzpatrick and Massa extinction relation. Three final models are presented here: SNEMO2, a two-component model for comparison with current Type Ia models; SNEMO7, a seven-component model chosen for standardizing supernova magnitudes, which results in a total dispersion of 0.100 mag for a validation set of supernovae, of which 0.087 mag is unexplained (a total dispersion of 0.113 mag with an unexplained dispersion of 0.097 mag is found for the total set of training and validation supernovae); and SNEMO15, a comprehensive 15-component model that maximizes the amount of spectral time-series behavior captured.