Installing packages to home directory with package manager

I have an account on a remote GNU+Linux system that I use via SSH, I have no root access to the machine. Sometimes I need more software or newer versions than provided by system administrators, so currently I install everything I need by hand in ~/opt directory, but it’s getting hard to maintain as number of packages installed increases. Is there any package manager (like apt, yum, portage) that can install stuff in my home directory instead of root?

I was looking for a similar thing recently, and found this blog post [1], which mentions using gentoo-prefix and nix prefix

[1] http://invalidmagic.wordpress.com/2011/01/21/running-the-nix-package-manager-in-a-prefix-as-the-home-directory/

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