The difficulty of finding the second derivatives of the likelihood function has meant that until now it has not been possible to use the usual Newton–Raphson approach to maximum‐likelihood estimation for the factor model. This paper gives a method of finding these second derivatives and shows how they lead to a simple and rapidly convergent numerical method for the estimation of factor model parameters. Some comparisons are made with another recent method due to Jöreskog&Lawley. A useful feature of the method is an asymptotically correct expression for the sampling variances of the estimated parame