In the world of technology, a landscape that shifts and evolves with every passing second, finding the right talent to navigate, negotiate, and nurture this landscape is paramount. The process of hiring a software engineer, one who is not just competent but stellar, is akin to mining for gold in an expansive, uncharted terrain.

Given the rapid progression of technology, software engineering has evolved into a multifaceted discipline incorporating a range of skills. A software engineer is not merely a coder or a programmer. They are an architect of digital solutions, a navigator of complex systems, a creative problem solver, and a relentless optimist. Each software engineer carries a toolbox that houses a distinct repertoire of skills, experience, and knowledge, empowering them to solve specific technological challenges.

In the quest to hire a stellar software engineer, there are certain parameters that need special attention, namely their technical prowess, problem-solving capabilities, versatility, and adaptability.

In terms of technical proficiency, it is vital to ensure that the candidate possesses a comprehensive understanding of data structures, algorithms, and system design. They should be proficient in at least one programming language, such as Python, Java, or C++. Knowledge of front-end technologies (like HTML, CSS, and JavaScript), back-end technologies (like Ruby, Node.js, or PHP), and database management systems is a significant add-on.

Problem-solving capabilities are the bedrock of software engineering. This involves the ability to dissect complex problems into manageable components, to think critically and logically, and to arrive at efficient solutions. Techniques such as Big-O notation, used to describe the performance or complexity of an algorithm, are crucial in this context.

Versatility is a desirable trait in a software engineer. This pertains to their ability to work with diverse technologies, languages, and platforms. Given the pace at which the tech landscape is changing, this reflects the engineer's capacity for continuous learning and growth.

Adaptability implies their ability to pivot quickly in response to changing requirements or unforeseen challenges. This quality becomes crucial in environments that follow agile methodologies, where the ability to respond to change is valued over sticking to a rigid plan.

Hiring a software engineer is no longer a transactional process. It is critical to ensure a cultural fit and alignment with organizational values. This includes aspects such as work ethic, communication skills, team dynamics, and a growth mindset. Herein, behavioral psychology can provide valuable insights. Concepts like the Pygmalion Effect, where high expectations lead to improved performance, can be harnessed to foster a conducive work environment post-hire.

The hiring process can greatly benefit from leveraging data analytics for screening and shortlisting candidates. The use of Machine Learning algorithms like Naive Bayes or Support Vector Machines to analyze resumes can help in identifying the most suitable candidates. Similarly, predictive analytics can provide insights into a candidate's future performance based on their past data.

It's also crucial to consider the law of diminishing returns - a concept borrowed from economics - while determining the optimal time and resources to be spent on the hiring process. There is a point beyond which investing more time in scrutinizing a candidate does not provide any additional value. Locating this point can streamline the hiring process and make it more efficient.

In conclusion, the quest to hire a stellar software engineer is a complex interplay of understanding technical competencies, problem-solving abilities, adaptability, versatility, and cultural fitment. The process warrants a thoughtful merging of technological insights, behavioral psychology, data analytics, and economic principles. It is only through a comprehensive and multi-faceted approach that we can find the polymath who can successfully navigate the shifting sands of the tech landscape.