Your best bet at this issue is to build Nginx from scratch.
Save your nginx config files before to a safe place and then do, assuming you are in Debian:
sudo dpkg -r nginx
If you are in Debian : sudo apt-get install build-essential zlib1g-dev libpcre3-dev
Just make sure you remove Nginx and get the needed libs to build Nginx from source if not in Debian.
The libs and tools are :
gcc-c++ pcre zlib make wget
This next part is system independent.
Get the latest Nginx version :
cd /usr/src/
sudo wget http://nginx.org/download/nginx-1.7.6.tar.gz
sudo tar xvfvz nginx-1.7.6.tar.gz
cd /usr/src/nginx-1.7.6
Get the latest pagespeed source:
sudo wget https://github.com/pagespeed/ngx_pagespeed/archive/v1.9.32.1-beta.zip
Unpack first the module :
sudo unzip v1.9.32.1-beta.zip
cd ngx_pagespeed-1.9.32.1-beta
Wget the PSOL libs inside the module dir and unpack them there:
sudo wget wget https://dl.google.com/dl/page-speed/psol/1.9.32.1.tar.gz
sudo tar xvfvz 1.9.32.1.tar.gz
cd back to the nginx source root dir and configure, make and make install. Make sure you change the Nginx user on the configuration stage to one that suits your needs (--user=nginx --group=nginx):
cd /usr/src/nginx-1.7.6
./configure --add-module=/usr/src/nginx-1.7.6/ngx_pagespeed-1.9.32.1-beta --prefix=/usr/local/nginx --sbin-path=/usr/local/sbin/nginx --conf-path=/etc/nginx/nginx.conf --error-log-path=/var/log/nginx/error.log --http-log-path=/var/log/nginx/access.log --pid-path=/run/nginx.pid --lock-path=/run/lock/subsys/nginx --user=nginx --group=nginx
When configure stage is done :
sudo make
sudo make install
That will get you the last Nginx version with the last pagespeed mod and libraries ready to rock.