JQuery multiple checkbox filtering multiple (more than 3) categories

I have to create a page that lists 19 courses. I would like to add filtering functionality to it that would allow a visitor to filter the courses by different characteristics (job function, date, duration, location, product, etc).

I came across this previous question on StackOverflow that came close to solving my problem. However the solution only has three sets of checkboxes and I need 8 sets.

I have some code on JSFiddle, which can filter the first three categories but beyond that it doesn't filter.

var byProperty = [], byColor = [], byLocation = [];

    $("input[name=cat1]").on( "change", function() {
        if (this.checked) byProperty.push("[data-category~='" + $(this).attr("value") + "']");
        else removeA(byProperty, "[data-category~='" + $(this).attr("value") + "']");
    });

    $("input[name=cat2]").on( "change", function() {
        if (this.checked) byColor.push("[data-category~='" + $(this).attr("value") + "']");
        else removeA(byColor, "[data-category~='" + $(this).attr("value") + "']");
    });

    $("input[name=cat3]").on( "change", function() {
        if (this.checked) byLocation.push("[data-category~='" + $(this).attr("value") + "']");
        else removeA(byLocation, "[data-category~='" + $(this).attr("value") + "']");
    });

    $("input").on( "change", function() {
        var str = "Include items \n";
        var selector = '', cselector = '', nselector = '';

        var $lis = $('.courses > div'),
            $checked = $('input:checked');  

        if ($checked.length) {  

            if (byProperty.length) {        
                if (str == "Include items \n") {
                    str += "    " + "with (" +  byProperty.join(',') + ")\n";               
                    $($('input[name=cat1]:checked')).each(function(index, byProperty){
                        if(selector === '') {
                            selector += "[data-category~='" + byProperty.id + "']";                     
                        } else {
                            selector += ",[data-category~='" + byProperty.id + "']";    
                        }                
                    });                 
                } else {
                    str += "    AND " + "with (" +  byProperty.join(' OR ') + ")\n";                
                    $($('input[name=cat2]:checked')).each(function(index, byProperty){
                        selector += "[data-category~='" + byProperty.id + "']";
                    });
                }                           
            }

            if (byColor.length) {                       
                if (str == "Include items \n") {
                    str += "    " + "with (" +  byColor.join(' OR ') + ")\n";                   
                    $($('input[name=cat2]:checked')).each(function(index, byColor){
                        if(selector === '') {
                            selector += "[data-category~='" + byColor.id + "']";                    
                        } else {
                            selector += ",[data-category~='" + byColor.id + "']";   
                        }                
                    });                 
                } else {
                    str += "    AND " + "with (" +  byColor.join(' OR ') + ")\n";               
                    $($('input[name=cat2]:checked')).each(function(index, byColor){
                        if(cselector === '') {
                            cselector += "[data-category~='" + byColor.id + "']";                   
                        } else {
                            cselector += ",[data-category~='" + byColor.id + "']";  
                        }                   
                    });
                }           
            }

            if (byLocation.length) {            
                if (str == "Include items \n") {
                    str += "    " + "with (" +  byLocation.join(' OR ') + ")\n";                
                    $($('input[name=cat3]:checked')).each(function(index, byLocation){
                        if(selector === '') {
                            selector += "[data-category~='" + byLocation.id + "']";                     
                        } else {
                            selector += ",[data-category~='" + byLocation.id + "']";    
                        }                
                    });             
                } else {
                    str += "    AND " + "with (" +  byLocation.join(' OR ') + ")\n";                
                    $($('input[name=cat3]:checked')).each(function(index, byLocation){
                        if(nselector === '') {
                            nselector += "[data-category~='" + byLocation.id + "']";                    
                        } else {
                            nselector += ",[data-category~='" + byLocation.id + "']";   
                        }   
                    });
                }            
            }

            $lis.hide(); 
            console.log(selector);
            console.log(cselector);
            console.log(nselector);

            if (cselector === '' && nselector === '') {         
                $('.courses > div').filter(selector).show();
            } else if (cselector === '') {
                $('.courses > div').filter(selector).filter(nselector).show();
            } else if (nselector === '') {
                $('.courses > div').filter(selector).filter(cselector).show();
            } else {
                $('.courses > div').filter(selector).filter(cselector).filter(nselector).show();
            }

        } else {
            $lis.show();
        }   

        $("#result").html(str); 

    });

    function removeA(arr) {
        var what, a = arguments, L = a.length, ax;
        while (L > 1 && arr.length) {
            what = a[--L];
            while ((ax= arr.indexOf(what)) !== -1) {
                arr.splice(ax, 1);
            }
        }
        return arr;
    }

How could I edit my code that would incorporate the remaining categories (4-8)?

Thanks!