Physical human-robot interaction plays an important role in social robotics, and touch is one of the key factors that influence a human's impression of robots. However, very few studies have explored different conditions pertaining to such interactions, and therefore, only few systematic results have been reported. As the first step toward addressing this issue, we studied the types of impressions of a robot's personality that humans may experience when they touch a soft part of the robot. In the study, the left forearm of a childlike android robot named "Affetto" was exposed; the original forearm was made of silicone rubber and can be replaced with any one of three other forearms that provide different sensations of hardness upon touching. Participants were asked to touch the robot's forearm and answer evaluation questionnaires on 19 touch sensations and 46 personality impressions for each of the four conditions associated with the different forearms. Four impression factors for touch sensations and three for personality impressions were extracted from the evaluation scores by the factor analysis method. The causal relationships between these factors were analyzed by the path analysis method. Several significant causal relationships were found, for example, between preferable touch sensations and likable personality impressions. The study results are expected to help in the design of the personality impressions of robots by facilitating a more systematic design of touch sensations. Furthermore, the results of an analysis of variance suggested that the most preferable touch sensation is possibly related to the robot's appearance and that designers of social robots should understand the complex touch sensation properties of humans.