Analyzing writing to explore the writer's psyche is not exclusive to professional writers. Any type of writing for work, school, or otherwise can offer some insight into what a writer is thinking if analyzed. "I think, therefore I am" is an idea widely used in philosophical circles, so it is no surprise that what you are thinking is widely acknowledged as being a direct insight into who you are. In the works of Sigmund Freud, he considered the subconscious as a powerful determiner of who we are and why we do what we do. Writing is a way of releasing the subconscious to offer insight into what makes us tick.
Analysis in this case cannot be superficial, as it may seem necessary. For example, just because a writer mentions a murder or even puts herself in the mindset of a killer does not make her a killer. Instead, it can hint at a writer's dissatisfaction with something in her life and the need to gain control. However, if a theme is recurring multiple times in an individual's writings, there could be a reason for this repetition, and further analysis might need to be considered.
There are several ways to find out more about what your writing says about you. One way is to start "free writing." This is the process of writing anything and everything you are thinking, with the complete absence of any previous planning. These "free writes" are often marked with sporadic prose as well as lines that have a more rhythmic and poetic quality. The point of this exercise is simply to write with a "shoot from the hip" mentality that prohibits the writer from putting up any guards or inhibitions. These samples will be perhaps the most telling, because they are one of the most honest works that a writer can offer.
One of the benefits of there being such a direct correlation between what we think and what we write about---as well as the way we go about writing it---is that it allows you to get a window into your own psyche. Often what you write during free association exercises, or even what you write with more rigid prompts, can display a lot about what you are thinking.
There is a belief, especially in the field of child psychology, that what we write can exhibit some of our deepest secrets, even if veiled in another context. For example, often child psychologists will encourage their patients to make free associations, create artwork, or write stories in response to prompting or when left to their own devices. Often what the child creates will offer insight into what the child is thinking, what the child is feeling, and even sometimes what the child has experienced, especially in regards to some sort of abuse or violent tendencies.