Language models are a key technology in various tasks, such as, speech recognition and machine translation. They are usually used on texts covering various domains and as a result domain adaptation has been a long ongoing challenge in language model research. With the rising popularity of neural network based language models, many methods have been proposed in recent years. These methods can be separated into two categories: model based and feature based adaptation methods. Feature based domain adaptation has compared to model based domain adaptation the advantage that it does not require domain labels in the corpus. Most existing feature based adaptation methods are based on bias adaptation. We propose a novel feature based domain adaptation technique using hidden layer factorisation. This method is fundamentally different from existing methods because we use the domain features to calculate a linear combination of linear layers. These linear layers can capture domain specific information and information common to different domains. In the experiments, we compare our proposed method with existing adaptation methods. The compared adaptation techniques are based on two different ideas, that is, bias based adaptation and gating of hidden units. All language models in our comparison use state-of-the-art long short-term memory based recurrent neural networks. We demonstrate the effectiveness of the proposed method with perplexity results for the well-known Penn Treebank and speech recognition results for a corpus of TED talks.