Abstract The variance reaction time model (VRTM) is proposed to account for various recognition data on reaction time, the mirror effect, receiver-operating-characteristic (ROC) curves, etc. The model is based on simple and plausible assumptions within a neural network: VRTM is a two layer neural network where one layer represents items and one layer represents contexts. The recognition decision is based on a random walk of nodes activated at recognition. VRTM suggests theoretical constraints on the distributions of nodes activated at recognition and the noise in the random walk. The variability in the net inputs to nodes depends on the item frequency (the number of times that the item has been encoded) and the list length. The essential mechanism that accounts for the empirical data is a non-linear activation function. The mean activation threshold in the non-linear activation function is placed to achieve efficient discriminability between new and old items and there is variability in the activation threshold. VRTM predicts the mirror effect for low and high frequency words, a strength based mirror effect between conditions but not within one condition, appropriate ROC-curves for old/new and high/low frequency items, and list-length effects. Furthermore, it predicts appropriate means and distributions of reaction times for old/new, correct/incorrect, and high/low frequency items as well as speed/accuracy tradeoffs. VRTM has an explicit mathematical solution, it is simulated in a neural network, and it is fitted to a number of datasets.