Align equations as if first term has operator (+ or -) in front

Question

I have a set of equations I'd like to align. Below is what it looks like now, but I'd prefer if I could have the first term after each equal sign align with the terms below, ignoring the operator below.

This is the code I'm using for the equation above:
begin{align}
ell
={}
&  mu_0 - y_0 log mu_0
&+ mu_b - y_b log mu_b
&+ mu_r - y_r log mu_r
&+ mu_{br} - y_{br} log mu_{br}[4pt]
={}
&  pi_0 U - y_0 log left( pi_0 U right)
&+ pi_b U d_b - y_b log left( pi_b U d_bright)
&+ pi_r U d_r - y_r log left( pi_r U d_r right) 
&+ pi_{br} U d_b d_r - y_{br} log left( pi_{br} U d_b d_r right) [4pt]
={}
&  left(pi_0 + pi_b d_b + pi_r d_r + pi_{br} d_b d_rright) U 
&- (y_0 + y_b + y_r + y_{br}) log U 
&- y_0 log pi_0 
&- y_b log left( pi_b d_b right) 
&- y_r log left( pi_r d_r right) 
&- y_{br} log left( pi_{br} d_b d_r right) 
end{align}

I'd like it to look like the image below (achieved with some image editing):

I've tried adding a phantom{+} in front of the first terms, and this does add some spacing, but it doesn't align correctly.
What's the best way to get the alignment I'm looking for?

egreg · Accepted Answer

You can use mathbin{vphantom{+}}, so the object will behave in everything like a +.
documentclass{article}
usepackage{amsmath}

begin{document}
begin{align}
ell={}
&mathbin{phantom{+}}  mu_0 - y_0 log mu_0
&+ mu_b - y_b log mu_b
&+ mu_r - y_r log mu_r
&+ mu_{br} - y_{br} log mu_{br}[4pt]
={}
&mathbin{phantom{+}}  pi_0 U - y_0 log ( pi_0 U )
&+ pi_b U d_b - y_b log ( pi_b U d_b)
&+ pi_r U d_r - y_r log ( pi_r U d_r ) 
&+ pi_{br} U d_b d_r - y_{br} log ( pi_{br} U d_b d_r ) [4pt]
={}
&mathbin{phantom{+}}  (pi_0 + pi_b d_b + pi_r d_r + pi_{br} d_b d_r) U 
&- (y_0 + y_b + y_r + y_{br}) log U 
&- y_0 log pi_0 
&- y_b log ( pi_b d_b ) 
&- y_r log ( pi_r d_r ) 
&- y_{br} log ( pi_{br} d_b d_r )
end{align}

end{document}

However, I like this like a punch in the eye, even if we remove all numbers, which I suspect you don't actually want, because the code is supposed to be fed to MathJax. I checked and it works also there.
Note that I removed all the left and right tokens, whose only effect in this case is to add unwanted spaces.
documentclass{article}
usepackage{amsmath}

begin{document}

begin{align*}
ell&=
         mu_0 - y_0 log mu_0
&qquad+ mu_b - y_b log mu_b
&qquad+ mu_r - y_r log mu_r
&qquad+ mu_{br} - y_{br} log mu_{br}[4pt]
&=
         pi_0 U - y_0 log ( pi_0 U )
&qquad+ pi_b U d_b - y_b log ( pi_b U d_b)
&qquad+ pi_r U d_r - y_r log ( pi_r U d_r ) 
&qquad+ pi_{br} U d_b d_r - y_{br} log ( pi_{br} U d_b d_r ) [4pt]
&=
         (pi_0 + pi_b d_b + pi_r d_r + pi_{br} d_b d_r) U 
&qquad- (y_0 + y_b + y_r + y_{br}) log U 
&qquad- y_0 log pi_0 
&qquad- y_b log ( pi_b d_b ) 
&qquad- y_r log ( pi_r d_r ) 
&qquad- y_{br} log ( pi_{br} d_b d_r )
end{align*}

end{document}

Align equations as if first term has operator (+ or -) in front

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