Recently, the Counting Grid (CG) model  was developed to represent each input image as a point in a large grid of feature counts. This latent point is a corner of a window of grid points which are all uniformly combined to match the (normalized) feature counts in the image. Being a bag of word model with spatial layout in the latent space, the CG model has superior handling of field of view changes in comparison to other bag of word models, but with the price of being essentially a mixture, mapping each scene to a single window in the grid. In this paper we introduce a family of componential models, dubbed the Componential Counting Grid, whose members represent each input image by multiple latent locations, rather than just one. In this way, we make a substantially more flexible admixture model which captures layers or parts of images and maps them to separate windows in a Counting Grid. We tested the models on scene and place classification where their componential nature helped to extract objects, to capture parallax effects, thus better fitting the data and outperforming Counting Grids and Latent Dirichlet Allocation, especially on sequences taken with wearable cameras.