This paper studies large dimensional factor models with threshold-type regime shifts in the loadings. We estimate the threshold by concentrated least squares, and factors and loadings by principal components. The estimator for the threshold is superconsistent, with convergence rate that depends on the time and cross-sectional dimensions of the panel, and it does not affect the estimator for factors and loadings: this has the same convergence rate as in linear factor models. We propose model selection criteria and a linearity test. Empirical application of the model shows that connectedness in financial variables increases during periods of high economic policy uncertainty.