I have already checked the other questions with on this issue, but since the problem seems to be very specific they weren't helpful.
I have a dataframe like this (this is just a quick example, example data from dput() is provided below):
year species abundance site county
2005 A 2 SH1 Göttingen
2006 A 0 SH1 Göttingen
2007 A NA SH1 Göttingen
2008 A 2 SH1 Göttingen
2009 A NA SH1 Göttingen
2010 A 2 SH1 Göttingen
2011 A NA SH1 Göttingen
2005 B 2 SH1 Göttingen
2006 B 0 SH1 Göttingen
2007 B NA SH1 Göttingen
2008 B 2 SH1 Göttingen
2009 B NA SH1 Göttingen
2010 B 2 SH1 Göttingen
2011 B NA SH1 Göttingen
2005 A 2 SH1 Göttingen
2006 A 0 SH1 Göttingen
2007 A NA SH1 Göttingen
2008 A 2 SH1 Göttingen
2009 A NA SH1 Göttingen
2010 A 2 SH1 Göttingen
2011 A NA SH1 Göttingen
2005 A 2 SH2 Göttingen
2006 A 0 SH2 Göttingen
2007 A NA SH2 Göttingen
2008 A 2 SH2 Göttingen
2009 A NA SH2 Göttingen
2010 A 2 SH2 Göttingen
2011 A NA SH2 Göttingen
It contains the abundance for 11 species on several different sites per county (more than 1500 sites in over 400ish counties) for each year 2005-2011. for each site, in every county, every year, all species have been accounted for, so there is either an NA, or a number in abundance for every year. The number of sites varies per county.
I would like to run the following loop to put the abundance into several columns: It should create a linear model to calculate population trends over these years and put the output in an additional row. In the end I would like to have a trend for every species on every site over the years:
alldata_lm$slope_abundance_plot <- NA
alldata_lm$p_slope_abundance_plot <- NA
species <- unique(alldata_lm$species)
sites <- unique(alldata_lm$site)
for (i in (1:length(species))) {
for (k in(1:length(sites))) {
print(c(i,k))
lm1 <- lm(abundance ~ year, data = alldata_lm[alldata_lm$species == species[i] & alldata_lm$site == sites[k],], na.action=na.omit)
alldata_lm$slope_abundance_plot[alldata_lm$species == species[i] & alldata_lm$site == sites[k]] <- coefficients(lm1)[2]
if (nrow(coef(summary(lm1)))>1){ alldata_lm$p_slope_abundance_plot[alldata_lm$species == species[i] & alldata_lm$site == sites[k]] <- coef(summary(lm1))[2,4]}
}
}
However, when I do, it returns the following error:
Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
alle Fälle NA
The same loop works perfectly with a very similar dataframe, the only difference is that the current dataframe contains far more NA's.
Deleting the NA's prior to running the loop does not help. I get the error message no matter if there are any NA's in the abundance column or not. I think the error might occur somewhere else. The year column does never contain any missing values.
I'd greatly appreciate any help! Thanks
EXAMPLE DATA
structure(list(site = structure(c(700L, 700L, 700L, 700L, 700L,
700L, 700L), .Label = c("bb1", "bb100", "bb101", "bb104", "bb107",
"bb108", "bb109", "bb11", "bb111", "bb113", "bb115", "bb116",
"bb117", "bb118", "bb119", "bb120", "bb121", "bb122", "bb123",
"bb124", "bb125", "bb126", "bb127", "bb129", "bb130", "bb131",
"bb132", "bb134", "bb135", "bb138", "bb139", "bb14", "bb140",
"bb143", "bb147", "bb15", "bb150", "bb152", "bb154", "bb155",
"bb156", "bb157", "bb158", "bb159", "bb163", "bb164", "bb166",
"bb167", "bb169", "bb170", "bb171", "bb172", "bb173", "bb174",
"bb175", "bb176", "bb177", "bb178", "bb179", "bb180", "bb181",
"bb183", "bb186", "bb187", "bb188", "bb19", "bb191", "bb192",
"bb193", "bb194", "bb197", "bb198", "bb199", "bb20", "bb200",
"bb201", "bb202", "bb203", "bb204", "bb205", "bb207", "bb208",
"bb209", "bb21", "bb210", "bb211", "bb212", "bb213", "bb215",
"bb216", "bb217", "bb218", "bb219", "bb220", "bb221", "bb224",
"bb225", "bb228", "bb23", "bb230", "bb232", "bb234", "bb237",
"bb239", "bb242", "bb27", "bb32", "bb35", "bb37", "bb38", "bb39",
"bb4", "bb40", "bb41", "bb47", "bb49", "bb53", "bb55", "bb58",
"bb59", "bb6", "bb60", "bb63", "bb65", "bb66", "bb7", "bb70",
"bb72", "bb73", "bb76", "bb77", "bb79", "bb8", "bb80", "bb81",
"bb82", "bb84", "bb85", "bb87", "bb89", "bb9", "bb90", "bb91",
"bb92", "bb93", "bb94", "bb96", "bb97", "bb98", "be14", "be15",
"be17", "be30", "bw10", "bw100", "bw104", "bw108", "bw111", "bw112",
"bw12", "bw120", "bw124", "bw126", "bw13", "bw144", "bw146",
"bw175", "bw183", "bw192", "bw193", "bw198", "bw199", "bw200",
"bw202", "bw208", "bw210", "bw211", "bw213", "bw215", "bw219",
"bw225", "bw226", "bw229", "bw236", "bw243", "bw257", "bw262",
"bw266", "bw268", "bw283", "bw294", "bw3", "bw30", "bw307", "bw326",
"bw327", "bw338", "bw339", "bw341", "bw35", "bw36", "bw360",
"bw368", "bw380", "bw381", "bw397", "bw405", "bw42", "bw53",
"bw58", "bw6", "bw7", "bw84", "bw89", "bw91", "bw92", "bw96",
"bw97", "by10", "by103", "by109", "by11", "by110", "by111", "by112",
"by113", "by114", "by115", "by116", "by117", "by118", "by120",
"by122", "by125", "by126", "by127", "by128", "by129", "by130",
"by134", "by137", "by14", "by142", "by144", "by146", "by147",
"by150", "by151", "by152", "by153", "by154", "by155", "by156",
"by157", "by158", "by159", "by163", "by164", "by166", "by167",
"by169", "by170", "by171", "by173", "by175", "by176", "by177",
"by178", "by18", "by180", "by182", "by186", "by187", "by188",
"by19", "by192", "by193", "by194", "by197", "by200", "by203",
"by205", "by210", "by212", "by215", "by22", "by222", "by223",
"by225", "by226", "by229", "by230", "by231", "by233", "by234",
"by236", "by238", "by239", "by24", "by240", "by241", "by242",
"by243", "by247", "by248", "by25", "by250", "by251", "by255",
"by257", "by267", "by268", "by271", "by272", "by274", "by275",
"by278", "by279", "by28", "by280", "by283", "by284", "by285",
"by286", "by287", "by289", "by29", "by290", "by291", "by292",
"by293", "by294", "by295", "by298", "by30", "by303", "by305",
"by307", "by308", "by310", "by32", "by321", "by322", "by323",
"by324", "by326", "by331", "by333", "by334", "by337", "by34",
"by341", "by346", "by347", "by350", "by352", "by356", "by357",
"by36", "by368", "by37", "by370", "by376", "by378", "by39", "by4",
"by40", "by41", "by43", "by451", "by452", "by47", "by5", "by52",
"by53", "by56", "by63", "by64", "by65", "by66", "by67", "by68",
"by69", "by7", "by72", "by74", "by76", "by79", "by8", "by80",
"by87", "by88", "by89", "by90", "by91", "by92", "by96", "by97",
"by98", "hb16", "hb17", "hb18", "hb21", "hb30", "hb5", "hb6",
"hb7", "hb9", "he100", "he103", "he106", "he107", "he108", "he109",
"he110", "he111", "he113", "he114", "he115", "he116", "he119",
"he120", "he122", "he124", "he13", "he130", "he137", "he14",
"he144", "he145", "he150", "he154", "he18", "he37", "he42", "he46",
"he47", "he51", "he52", "he66", "he68", "he7", "he70", "he72",
"he73", "he75", "he82", "he83", "he84", "he85", "he89", "he9",
"he91", "he93", "he94", "he96", "he97", "hh10", "hh28", "hh29",
"hh30", "hh41", "hh44", "mv108", "mv109", "mv110", "mv122", "mv124",
"mv125", "mv126", "mv141", "mv143", "mv15", "mv153", "mv156",
"mv160", "mv17", "mv24", "mv29", "mv40", "mv41", "mv50", "mv55",
"mv61", "mv63", "mv76", "mv82", "ni10", "ni100", "ni101", "ni102",
"ni11", "ni110", "ni111", "ni119", "ni122", "ni125", "ni126",
"ni13", "ni131", "ni134", "ni135", "ni136", "ni138", "ni14",
"ni142", "ni146", "ni147", "ni149", "ni15", "ni150", "ni152",
"ni162", "ni163", "ni166", "ni167", "ni168", "ni169", "ni170",
"ni171", "ni172", "ni175", "ni182", "ni187", "ni188", "ni189",
"ni191", "ni192", "ni193", "ni198", "ni2", "ni20", "ni206", "ni215",
"ni218", "ni225", "ni226", "ni227", "ni231", "ni236", "ni239",
"ni240", "ni241", "ni242", "ni243", "ni244", "ni246", "ni252",
"ni257", "ni26", "ni260", "ni263", "ni272", "ni274", "ni282",
"ni286", "ni290", "ni291", "ni297", "ni298", "ni299", "ni3",
"ni303", "ni32", "ni34", "ni37", "ni38", "ni39", "ni4", "ni40",
"ni41", "ni43", "ni45", "ni453", "ni455", "ni46", "ni47", "ni49",
"ni50", "ni52", "ni55", "ni6", "ni61", "ni63", "ni66", "ni68",
"ni71", "ni72", "ni73", "ni76", "ni77", "ni85", "ni87", "ni88",
"ni89", "ni90", "ni91", "ni92", "ni93", "ni95", "ni97", "nw10",
"nw108", "nw110", "nw112", "nw126", "nw13", "nw130", "nw140",
"nw142", "nw143", "nw149", "nw154", "nw156", "nw173", "nw182",
"nw20", "nw25", "nw38", "nw41", "nw5", "nw50", "nw52", "nw53",
"nw54", "nw55", "nw6", "nw60", "nw63", "nw7", "nw72", "nw73",
"nw74", "nw84", "nw86", "nw92", "rp101", "rp102", "rp103", "rp106",
"rp108", "rp109", "rp116", "rp117", "rp120", "rp130", "rp131",
"rp139", "rp140", "rp143", "rp144", "rp146", "rp21", "rp22",
"rp23", "rp24", "rp36", "rp4", "rp84", "rp94", "rp99", "sh100",
"sh101", "sh102", "sh103", "sh106", "sh109", "sh11", "sh111",
"sh112", "sh117", "sh12", "sh121", "sh123", "sh125", "sh128",
"sh130", "sh132", "sh14", "sh140", "sh17", "sh18", "sh19", "sh20",
"sh25", "sh26", "sh27", "sh30", "sh33", "sh34", "sh35", "sh36",
"sh37", "sh39", "sh42", "sh43", "sh44", "sh45", "sh46", "sh47",
"sh51", "sh52", "sh54", "sh55", "sh58", "sh59", "sh60", "sh61",
"sh62", "sh63", "sh65", "sh66", "sh67", "sh69", "sh70", "sh71",
"sh72", "sh73", "sh74", "sh75", "sh76", "sh78", "sh79", "sh8",
"sh84", "sh86", "sh88", "sh89", "sh91", "sh93", "sh95", "sh96",
"sh98", "sh99", "sn104", "sn112", "sn117", "sn120", "sn123",
"sn131", "sn141", "sn144", "sn145", "sn15", "sn151", "sn158",
"sn159", "sn16", "sn162", "sn164", "sn165", "sn167", "sn18",
"sn25", "sn27", "sn28", "sn30", "sn35", "sn40", "sn44", "sn45",
"sn5", "sn56", "sn69", "sn7", "sn72", "sn74", "sn79", "sn83",
"sn87", "sn89", "sn9", "sn91", "sn92", "sn93", "sn99", "st1",
"st100", "st101", "st103", "st105", "st107", "st108", "st109",
"st11", "st110", "st111", "st112", "st113", "st114", "st115",
"st116", "st118", "st119", "st120", "st121", "st125", "st126",
"st127", "st13", "st130", "st134", "st135", "st137", "st139",
"st140", "st141", "st143", "st144", "st145", "st146", "st147",
"st148", "st150", "st151", "st153", "st158", "st159", "st160",
"st162", "st166", "st21", "st24", "st25", "st26", "st27", "st28",
"st30", "st33", "st34", "st4", "st43", "st47", "st49", "st50",
"st55", "st56", "st57", "st59", "st60", "st61", "st64", "st69",
"st70", "st72", "st75", "st77", "st79", "st84", "st87", "st88",
"st91", "st92", "st97", "st98", "st99", "th100", "th103", "th104",
"th105", "th112", "th118", "th121", "th123", "th15", "th16",
"th18", "th19", "th20", "th22", "th26", "th27", "th31", "th32",
"th36", "th39", "th4", "th40", "th44", "th45", "th49", "th50",
"th51", "th52", "th55", "th56", "th58", "th59", "th60", "th61",
"th63", "th64", "th73", "th76", "th8", "th81", "th83", "th85",
"th91", "th94", "th95", "th96", "th98", "th99"), class = "factor"),
year = 2005:2011, species = structure(c(8L, 8L, 8L, 8L, 8L,
8L, 8L), .Label = c("common linnet", "common whitethroat",
"corn bunting", "eurasian skylark", "northern lapwing", "red-backed shrike",
"tree sparrow", "western yellow wagtail", "whinchat", "woodlark",
"yellowhammer"), class = "factor"), abundance = c(NA_integer_,
NA_integer_, NA_integer_, NA_integer_, NA_integer_, NA_integer_,
NA_integer_), county = structure(c(48L, 48L, 48L, 48L, 48L,
48L, 48L), .Label = c("Aichach-Friedberg, Landkreis", "Alb-Donau-Kreis",
"Altmarkkreis Salzwedel", "Alzey-Worms, Landkreis", "Amberg-Sulzbach, Landkreis",
"Ammerland, Landkreis", "Anhalt-Bitterfeld, Landkreis", "Ansbach, Landkreis",
"Aschaffenburg, Landkreis", "Augsburg, Landkreis", "Aurich, Landkreis",
"Böblingen, Landkreis", "Börde, Landkreis", "Bad Dürkheim, Landkreis",
"Bad Kissingen, Landkreis", "Bad Kreuznach, Landkreis", "Bad Tölz-Wolfratshausen, Landkreis",
"Barnim, Landkreis", "Bautzen, Landkreis", "Bayreuth", "Bayreuth, Landkreis",
"Bergstraße, Landkreis", "Berlin", "Biberach, Landkreis",
"Bodenseekreis", "Borken, Kreis", "Brandenburg an der Havel, Kreisfreie Stadt",
"Breisgau-Hochschwarzwald, Landkreis", "Bremen, Kreisfreie Stadt",
"Bremerhaven, Kreisfreie Stadt", "Burgenlandkreis", "Calw, Landkreis",
"Celle, Landkreis", "Cham, Landkreis", "Chemnitz, Stadt",
"Cloppenburg, Landkreis", "Coburg, Landkreis", "Cottbus, Kreisfreie Stadt",
"Cuxhaven, Landkreis", "Dachau, Landkreis", "Dahme-Spreewald, Landkreis",
"Darmstadt-Dieburg, Landkreis", "Deggendorf, Landkreis",
"Dessau-Roßlau, Kreisfreie Stadt", "Diepholz, Landkreis",
"Dillingen a.d.Donau, Landkreis", "Dingolfing-Landau, Landkreis",
"Dithmarschen, Landkreis", "Donau-Ries, Landkreis", "Donnersbergkreis",
"Dresden, Stadt", "Ebersberg, Landkreis", "Eichsfeld, Kreis",
"Eichstätt, Landkreis", "Eisenach, krsfr. Stadt", "Elbe-Elster, Landkreis",
"Emmendingen, Landkreis", "Emsland, Landkreis", "Ennepe-Ruhr-Kreis",
"Enzkreis", "Erding, Landkreis", "Erfurt, krsfr. Stadt",
"Erlangen-Höchstadt, Landkreis", "Erzgebirgskreis", "Esslingen, Landkreis",
"Fürstenfeldbruck, Landkreis", "Fürth, Landkreis", "Forchheim, Landkreis",
"Frankfurt (Oder), Kreisfreie Stadt", "Frankfurt am Main, Kreisfreie Stadt",
"Freising, Landkreis", "Freudenstadt, Landkreis", "Freyung-Grafenau, Landkreis",
"Friesland, Landkreis", "Fulda, Landkreis", "Göppingen, Landkreis",
"Görlitz, Landkreis", "Göttingen, Landkreis", "Garmisch-Partenkirchen, Landkreis",
"Gießen, Landkreis", "Gifhorn, Landkreis", "Goslar, Landkreis",
"Gotha, Kreis", "Grafschaft Bentheim, Landkreis", "Greiz, Kreis",
"Höxter, Kreis", "Haßberge, Landkreis", "Halle (Saale), Kreisfreie Stadt",
"Hamburg", "Hameln-Pyrmont, Landkreis", "Hamm, Kreisfreie Stadt",
"Harburg, Landkreis", "Harz, Landkreis", "Havelland, Landkreis",
"Heidekreis, Landkreis", "Heidelberg, Kreisfreie Stadt",
"Heidenheim, Landkreis", "Heilbronn, Landkreis", "Heinsberg, Kreis",
"Hersfeld-Rotenburg, Landkreis", "Herzogtum Lauenburg, Landkreis",
"Hildburghausen, Kreis", "Hildesheim, Landkreis", "Hochsauerlandkreis",
"Hochtaunuskreis", "Hof, Landkreis", "Holzminden, Landkreis",
"Ilm-Kreis", "Ingolstadt", "Jerichower Land, Landkreis",
"Köln, Kreisfreie Stadt", "Kaiserslautern, Landkreis", "Karlsruhe, Kreisfreie Stadt",
"Karlsruhe, Landkreis", "Kassel, Landkreis", "Kelheim, Landkreis",
"Kitzingen, Landkreis", "Kleve, Kreis", "Konstanz, Landkreis",
"Kronach, Landkreis", "Kulmbach, Landkreis", "Kusel, Landkreis",
"Kyffhäuserkreis", "Lörrach, Landkreis", "Lüchow-Dannenberg, Landkreis",
"Lüneburg, Landkreis", "Lahn-Dill-Kreis", "Landkreis Ludwigslust-Parchim",
"Landkreis Mecklenburgische Seenplatte", "Landkreis Nordwestmecklenburg",
"Landkreis Rostock", "Landkreis Vorpommern-Greifswald", "Landkreis Vorpommern-Rügen",
"Landsberg am Lech, Landkreis", "Landshut, Landkreis", "Leer, Landkreis",
"Leipzig, Landkreis", "Lichtenfels, Landkreis", "Limburg-Weilburg, Landkreis",
"Lippe, Kreis", "Ludwigsburg, Landkreis", "Märkisch-Oderland, Landkreis",
"Märkischer Kreis", "Mühldorf a.Inn, Landkreis", "München, Landeshauptstadt",
"München, Landkreis", "Main-Spessart, Landkreis", "Main-Tauber-Kreis",
"Main-Taunus-Kreis", "Mainz-Bingen, Landkreis", "Mannheim, Universitätsstadt, Kreisfreie Stadt",
"Mansfeld-Südharz, Landkreis", "Marburg-Biedenkopf, Landkreis",
"Mayen-Koblenz, Landkreis", "Meißen, Landkreis", "Mettmann, Kreis",
"Minden-Lübbecke, Kreis", "Mittelsachsen, Landkreis", "Nürnberg",
"Nürnberger Land, Landkreis", "Neckar-Odenwald-Kreis", "Neu-Ulm, Landkreis",
"Neuburg-Schrobenhausen, Landkreis", "Neumarkt i.d.OPf., Landkreis",
"Neustadt a.d.Aisch-Bad Windsheim, Landkreis", "Neustadt a.d.Waldnaab, Landkreis",
"Neustadt an der Weinstraße, Kreisfreie Stadt", "Neuwied, Landkreis",
"Nienburg (Weser), Landkreis", "Nordfriesland, Landkreis",
"Nordhausen, Kreis", "Nordsachsen, Landkreis", "Northeim, Landkreis",
"Oberallgäu, Landkreis", "Oberhavel, Landkreis", "Oberspreewald-Lausitz, Landkreis",
"Odenwaldkreis", "Oder-Spree, Landkreis", "Offenbach, Landkreis",
"Oldenburg, Landkreis", "Olpe, Kreis", "Ortenaukreis", "Osnabrück, Landkreis",
"Ostalbkreis", "Ostallgäu, Landkreis", "Osterholz, Landkreis",
"Osterode am Harz, Landkreis", "Ostholstein, Landkreis",
"Ostprignitz-Ruppin, Landkreis", "Passau, Landkreis", "Peine, Landkreis",
"Pfaffenhofen a.d.Ilm, Landkreis", "Pinneberg, Landkreis",
"Plön, Landkreis", "Potsdam-Mittelmark, Landkreis", "Potsdam, Kreisfreie Stadt",
"Prignitz, Landkreis", "Rastatt, Landkreis", "Ravensburg, Landkreis",
"Regen, Landkreis", "Regensburg, Landkreis", "Region Hannover, Landkreis",
"Rems-Murr-Kreis", "Rendsburg-Eckernförde, Landkreis", "Reutlingen, Landkreis",
"Rhön-Grabfeld, Landkreis", "Rhein-Kreis Neuss", "Rhein-Neckar-Kreis",
"Rhein-Sieg-Kreis", "Rheingau-Taunus-Kreis", "Rheinisch-Bergischer Kreis",
"Rosenheim, Landkreis", "Rotenburg (Wümme), Landkreis",
"Roth, Landkreis", "Rottweil, Landkreis", "Sächsische Schweiz-Osterzgebirge, Landkreis",
"Sömmerda, Kreis", "Südliche Weinstraße, Landkreis", "Südwestpfalz, Landkreis",
"Saale-Holzland-Kreis", "Saale-Orla-Kreis", "Saalekreis",
"Saalfeld-Rudolstadt, Kreis", "Salzlandkreis", "Schaumburg, Landkreis",
"Schleswig-Flensburg, Landkreis", "Schmalkalden-Meiningen, Kreis",
"Schwabach", "Schwandorf, Landkreis", "Schweinfurt", "Schweinfurt, Landkreis",
"Segeberg, Landkreis", "Siegen-Wittgenstein, Kreis", "Sigmaringen, Landkreis",
"Soest, Kreis", "Sonneberg, Kreis", "Spree-Neiße, Landkreis",
"Stade, Landkreis", "Starnberg, Landkreis", "Steinburg, Landkreis",
"Steinfurt, Kreis", "Stendal, Landkreis", "Stormarn, Landkreis",
"Straubing-Bogen, Landkreis", "Stuttgart, Landeshauptstadt, Kreisfreie Stadt",
"Tübingen, Landkreis", "Teltow-Fläming, Landkreis", "Traunstein, Landkreis",
"Uckermark, Landkreis", "Uelzen, Landkreis", "Unstrut-Hainich-Kreis",
"Unterallgäu, Landkreis", "Vechta, Landkreis", "Verden, Landkreis",
"Viersen, Kreis", "Vogelsbergkreis", "Würzburg, Landkreis",
"Waldeck-Frankenberg, Landkreis", "Wartburgkreis", "Weißenburg-Gunzenhausen, Landkreis",
"Weilheim-Schongau, Landkreis", "Weimar, krsfr. Stadt", "Weimarer Land, Kreis",
"Werra-Meißner-Kreis", "Wesel, Kreis", "Wesermarsch, Landkreis",
"Westerwaldkreis", "Wetteraukreis", "Wiesbaden, Landeshauptstadt, Kreisfreie Stadt",
"Wittenberg, Landkreis", "Wittmund, Landkreis", "Wolfenbüttel, Landkreis",
"Wuppertal, Kreisfreie Stadt", "Zollernalbkreis", "Zwickau, Landkreis"
), class = "factor"), slope_abundance_plot = c(NA_real_,
NA_real_, NA_real_, NA_real_, NA_real_, NA_real_, NA_real_
), p_slope_abundance_plot = c(NA_real_, NA_real_, NA_real_,
NA_real_, NA_real_, NA_real_, NA_real_)), .Names = c("site",
"year", "species", "abundance", "county", "slope_abundance_plot",
"p_slope_abundance_plot"), row.names = c(61L, 75L, 76L, 91L,
92L, 93L, 134L), class = "data.frame")
