user-1: I believe I have read within the Dalai Lama's works that there exists (at least) two kinds of compassion meditation:

Generating the four abodes within oneself, in a more concentrative and affective way (metta bhavana). 
Analyzing compassion through logical discernment, having compassion as meditative object.

I noticed my capacity to be compassionate with analysis seems very limited. The Dalai Lama suggests to focus on feeling after using reasons to generate compassion. 
Is it possible that my mind functions more with feeling, and that analysis doesn't generate as much compassion in myself? What is the best course of action to generate compassion?

user-1: I wouldn't like to comment on exactly what the Buddha had in mind by this idea of generating compassion by analysis but it makes sense that if his view is philosophically sound then analysis will lead us towards it. 
I believe this is the case, such that if we analyse the doctrine philosophically we will start to see genuine reasons and motives for compassion in the unity and shared identity of sentient beings. On a simpler level it is easy to contemplate the similar situation in which all sentient beings find themselves and thus be led to a compassionate view. Thus analysis would lead to feelings would lead to compassion.  
But analysis may be a rather weak method in the end, just as you suspect, in the absence of feelings and the pursuit of insight. It seems best to use all the methods at our disposal. Perhaps the difference is that analysis and contemplation produces an object of compassion, whereas other approaches may be better at developing compassion as a phenomenon in itself. The former may see compassion as a relationship, the latter as a stand-alone feature of reality. (Rather as love can be seen in these two ways).        
This is rather speculative and hasty answer and may meet some objections. In marketing speak I'll run it up the flagpole and see if it flutters.     

user14872: The more you contemplate on the Noble Truth of Suffering (dukka) and understand the suffering in each plane, the better you will be able to spread loving kindness. Because when you say "May all beings in the Eastern direction be free from Suffering" and so on, if you have seen and contemplated on suffering in each of those worlds (hell, animal, peta, asura, human, all deva worlds & all brahma worlds) you truly feel compassion towards all living beings. The more you practice, it is as if you could replace each of those beings or worlds with the word "dukka" and you start to see without differentiating that everyone who is born is suffering. (And your mind will be fixed on Nibbana as well).
Also, when you spread loving kindness, do NOT spread it to yourself. No where in any discourse does the Buddha says to spread loving kindness to your self. All the places when Buddha talks about metta, he says to spread loving kindness to all beings in each directions. (metta sutta, vattupama sutta, mettakatha in patisambhidamagga, etc).
A good discourse to learn that will help practice loving kindness is the metta-sutta (in Suttanipata). Try this Metta Sutta Meditation You will learn in great detail how to practice loving kindness, all the way up to Nibbana.
With Metta

-1: <p>I believe I have read within the Dalai Lama's works that there exists (at least) two kinds of compassion meditation:</p>

<ul>
<li>Generating the four abodes within oneself, in a more concentrative and affective way (<em>metta bhavana</em>). </li>
<li>Analyzing compassion through logical discernment, having compassion as meditative object.</li>
</ul>

<p>I noticed my capacity to be compassionate with analysis seems very limited. The Dalai Lama suggests to focus on <em>feeling</em> after using reasons to generate compassion. </p>

<p><strong>Is it possible that my mind functions more with feeling, and that analysis doesn't generate as much compassion in myself? What is the best course of action to generate compassion?</strong></p>
 -1: <p>I wouldn't like to comment on exactly what the Buddha had in mind by this idea of generating compassion by analysis but it makes sense that if his view is philosophically sound then analysis will lead us towards it. </p>

<p>I believe this is the case, such that if we analyse the doctrine philosophically we will start to see genuine reasons and motives for compassion in the unity and shared identity of sentient beings. On a simpler level it is easy to contemplate the similar situation in which all sentient beings find themselves and thus be led to a compassionate view. Thus analysis would lead to feelings would lead to compassion.  </p>

<p>But analysis may be a rather weak method in the end, just as you suspect, in the absence of feelings and the pursuit of insight. It seems best to use all the methods at our disposal. Perhaps the difference is that analysis and contemplation produces an object of compassion, whereas other approaches may be better at developing compassion as a phenomenon in itself. The former may see compassion as a relationship, the latter as a stand-alone feature of reality. (Rather as love can be seen in these two ways).        </p>

<p>This is rather speculative and hasty answer and may meet some objections. In marketing speak I'll run it up the flagpole and see if it flutters.     </p>
 14872: <p>The more you contemplate on the Noble Truth of Suffering (dukka) and understand the suffering in each plane, the better you will be able to spread loving kindness. Because when you say "May all beings in the Eastern direction be free from Suffering" and so on, if you have seen and contemplated on suffering in each of those worlds (hell, animal, peta, asura, human, all deva worlds &amp; all brahma worlds) you truly feel compassion towards all living beings. The more you practice, it is as if you could replace each of those beings or worlds with the word "dukka" and you start to see without differentiating that everyone who is <em>born is suffering</em>. (And your mind will be fixed on Nibbana as well).</p>

<p>Also, when you spread loving kindness, do NOT spread it to yourself. No where in any discourse does the Buddha says to spread loving kindness to your self. All the places when Buddha talks about metta, he says to spread loving kindness to all beings in each directions. (metta sutta, vattupama sutta, mettakatha in patisambhidamagga, etc).</p>

<p>A good discourse to learn that will help practice loving kindness is the metta-sutta (in Suttanipata). Try this <a href="https://visuddhimagga.info/download.php?file=https://anaalaya.blob.core.windows.net/dhamma2018/M_E_MettaSutta_31_03_2018.mp3" rel="nofollow noreferrer">Metta Sutta Meditation</a> You will learn in great detail how to practice loving kindness, all the way up to Nibbana.</p>

<p>With Metta</p>
