Because of the commonly euphoric support of native players through the crowd at ATP tournaments it is likely to assume that those players have a small advantage over other players and thus win more matches against favorites easier than on "neutral" ground.
To find an answer to that question I examined all matches played in the years 1991 to 1997. I found out that among those players who both played matches in their native country and in other countries were...

... 211 players with a better match record,
...  48 players with an equal match record,
... 190 players with a worse match record

at tournaments in their native country compared to tournaments in other countries. Or, to say it in a different way, 47% of the players had an advantage in their native country, 42% had a disadvantage. You cannot claim that there are significantly more players who have an advantage than there are players who have a disadvantage. The figures are within the limits of a random distribution. Nevertheless, the tendency is leaning towards an "advantage".

To compare the different countries to each other there are two ways:

1. What percentage of players of a country have a better match record in their native country than in other countries?

Country    total players   players with disadv.   players with adv.

GB               11             1    9,09%           10   90,91%
BRA               5             1   20.00%            4   80.00%
NZL               5             0    0.00%            4   80.00%
ISR               7             1   14.29%            5   71.43%
AUT              10             1   10.00%            7   70.00%
MEX               6             1   16.67%            4   66.67%
RSA              11             4   36.36%            7   63.64%
RUS               8             2   25.00%            5   62.50%
ESP              40            15   37.50%           21   52.50%
BEL               6             2   33.33%            3   50.00%
JAP               6             1   16.67%            3   50.00%
USA              85            37   43.53%           38   44.71%
CAN               7             4   57.14%            3   42.86%
SWE              32            18   56.25%           13   40.63%
FRA              37            15   40.54%           15   40.54%
NED              18            10   55.56%            7   38.89%
ITA              21            10   47.62%            8   38.10%
GER              38            20   52.63%           13   34.21%
ARG              12             7   58.33%            4   33.33%
AUS              27            16   59.26%            9   33.33%
CZE              19            10   52.63%            6   31.58%
SUI               6             4   66.67%            1   16.67%

That means: The most native players gain an advantage (no matter how small it is) at tournaments in Great Britain.

2. How high are the average advantages of the different countries?

"Advantage" is defined here as the difference of the match percentage in the native country and the match percentage in other countries. Assumed that a player won 66% of his matches in his native country and only 40% of his matches in other countries. His advantage would be 26%.
Among all players of a country who had an advantage in their native country the average advantage was calculated.

Country   Advantage

MEX        29.42%
NZL        18.50%
ISR        18.24%
AUT        16.70%
ARG        16.53%
FRA        16.07%
GB         15.88%
CZE        15.78%
RSA        15.41%
RUS        15.12%
BRA        14.12%
ESP        13.74%
AUS        13.14%
USA        12.87%
SWE        11.85%
GER        10.41%
ITA         9.81%
NED         8.71%

That means: If a Mexican player has a home court advantage, then he has the highest average advantage among all countries.